Rewrite the equation as <math><mstyle displaystyle="true"><mo>-</mo><mn>16</mn><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>96</mn><mi>t</mi><mo>=</mo><mi>s</mi></mstyle></math> .

Move <math><mstyle displaystyle="true"><mi>s</mi></mstyle></math> to the left side of the equation by subtracting it from both sides.

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mo>-</mo><mn>16</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>96</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mo>-</mo><mi>s</mi></mstyle></math> into the quadratic formula and solve for <math><mstyle displaystyle="true"><mi>t</mi></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>96</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>16</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9216</mn><mo>-</mo><mn>64</mn><mi>s</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>9216</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>64</mn><mi>s</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>64</mn><mrow><mo>(</mo><mn>144</mn><mo>)</mo></mrow><mo>+</mo><mn>64</mn><mrow><mo>(</mo><mo>-</mo><mi>s</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>64</mn><mrow><mo>(</mo><mn>144</mn><mo>-</mo><mi>s</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mn>12</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mi>s</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>12</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Raise <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>16</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>96</mn><mo>±</mo><mn>8</mn><msqrt><mn>144</mn><mo>-</mo><mi>s</mi></msqrt></mrow><mrow><mo>-</mo><mn>32</mn></mrow></mfrac></mstyle></math> .

The final answer is the combination of both solutions.

Do you know how to Solve for t s=-16t^2+96t? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion four hundred fifty-nine million six hundred seventeen thousand two hundred seventy-four |
---|

- 1459617274 has 8 divisors, whose sum is
**2190742740** - The reverse of 1459617274 is
**4727169541** - Previous prime number is
**1669**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | four hundred twenty million nine hundred ninety-eight thousand seven hundred ninety-nine |
---|

- 420998799 has 4 divisors, whose sum is
**431793680** - The reverse of 420998799 is
**997899024** - Previous prime number is
**39**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 57
- Digital Root 3

Name | one billion six hundred ninety-one million eight hundred sixty-nine thousand six hundred twenty-three |
---|

- 1691869623 has 4 divisors, whose sum is
**2255826168** - The reverse of 1691869623 is
**3269681961** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 51
- Digital Root 6