Solve Using the Quadratic Formula 2x^2+7x=-6

$2 x^{2} + 7 x = - 6$

Step 1

Add $6$ to both sides of the equation.

$2 x^{2} + 7 x + 6 = 0$

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 $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (2 \cdot 6)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 6$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 8 \cdot 6}}{2 \cdot 2}$

Multiply $- 8$ by $6$ .

$x = \frac{- 7 \pm \sqrt{49 - 48}}{2 \cdot 2}$

Subtract $48$ from $49$ .

$x = \frac{- 7 \pm \sqrt{1}}{2 \cdot 2}$

Any root of $1$ is $1$ .

$x = \frac{- 7 \pm 1}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 7 \pm 1}{4}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{3}{2}, - 2$