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.

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