Solve Using the Quadratic Formula 2x^2+7x=9

$2 x^{2} + 7 x = 9$

Step 1

Subtract $9$ from both sides of the equation.

$2 x^{2} + 7 x - 9 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 2$ , $b = 7$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (2 \cdot - 9)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 2 \cdot - 9}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 9$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 8 \cdot - 9}}{2 \cdot 2}$

Multiply $- 8$ by $- 9$ .

$x = \frac{- 7 \pm \sqrt{49 + 72}}{2 \cdot 2}$

Add $49$ and $72$ .

$x = \frac{- 7 \pm \sqrt{121}}{2 \cdot 2}$

Rewrite $121$ as $11^{2}$ .

$x = \frac{- 7 \pm \sqrt{11^{2}}}{2 \cdot 2}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 7 \pm 11}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 7 \pm 11}{4}$

Step 5

The final answer is the combination of both solutions.

$x = 1, - \frac{9}{2}$