Solve Using the Quadratic Formula 2x^2-3x=7

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Algebra

$2 x^{2} - 3 x = 7$

Subtract $7$ from both sides of the equation.

$2 x^{2} - 3 x - 7 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 2$ , $b = - 3$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (2 \cdot - 7)}}{2 \cdot 2}$

Simplify.

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Simplify the numerator.

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Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 2 \cdot - 7}}{2 \cdot 2}$

Multiply $- 4$ by $2$ .

$x = \frac{3 \pm \sqrt{9 - 8 \cdot - 7}}{2 \cdot 2}$

Multiply $- 8$ by $- 7$ .

$x = \frac{3 \pm \sqrt{9 + 56}}{2 \cdot 2}$

Add $9$ and $56$ .

$x = \frac{3 \pm \sqrt{65}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{3 \pm \sqrt{65}}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{65}}{4}$

Decimal Form:

$x = 2.76556443 \dots, - 1.26556443 \dots$

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Name

Name	one billion three hundred fifty-nine million two hundred seventy-seven thousand eighty

Interesting facts

1359277080 has 128 divisors, whose sum is 8388686592
The reverse of 1359277080 is 0807729531
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	one billion one hundred twelve million three hundred seventy-six thousand nine hundred seventy-nine

Interesting facts

1112376979 has 8 divisors, whose sum is 1135767600
The reverse of 1112376979 is 9796732111
Previous prime number is 1913

Basic properties

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

Name

Name	one billion nine hundred fifty-four million seven hundred ninety thousand one hundred sixty-three

Interesting facts

1954790163 has 8 divisors, whose sum is 3475182528
The reverse of 1954790163 is 3610974591
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

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