Solve Using the Quadratic Formula 6x^2+7x=24

$6 x^{2} + 7 x = 24$

Step 1

Subtract $24$ from both sides of the equation.

$6 x^{2} + 7 x - 24 = 0$

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 $a = 6$ , $b = 7$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (6 \cdot - 24)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 6 \cdot - 24}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 24$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 7 \pm \sqrt{49 - 24 \cdot - 24}}{2 \cdot 6}$

Multiply $- 24$ by $- 24$ .

$x = \frac{- 7 \pm \sqrt{49 + 576}}{2 \cdot 6}$

Add $49$ and $576$ .

$x = \frac{- 7 \pm \sqrt{625}}{2 \cdot 6}$

Rewrite $625$ as $25^{2}$ .

$x = \frac{- 7 \pm \sqrt{25^{2}}}{2 \cdot 6}$

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

$x = \frac{- 7 \pm 25}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 7 \pm 25}{12}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{2}, - \frac{8}{3}$