Solve Using the Quadratic Formula 3x^2-14x=24

$3 x^{2} - 14 x = 24$

Step 1

Subtract $24$ from both sides of the equation.

$3 x^{2} - 14 x - 24 = 0$

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 $a = 3$ , $b = - 14$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{14 \pm \sqrt{{(- 14)}^{2} - 4 \cdot (3 \cdot - 24)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 14$ to the power of $2$ .

$x = \frac{14 \pm \sqrt{196 - 4 \cdot 3 \cdot - 24}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 24$ .

Multiply $- 4$ by $3$ .

$x = \frac{14 \pm \sqrt{196 - 12 \cdot - 24}}{2 \cdot 3}$

Multiply $- 12$ by $- 24$ .

$x = \frac{14 \pm \sqrt{196 + 288}}{2 \cdot 3}$

Add $196$ and $288$ .

$x = \frac{14 \pm \sqrt{484}}{2 \cdot 3}$

Rewrite $484$ as $22^{2}$ .

$x = \frac{14 \pm \sqrt{22^{2}}}{2 \cdot 3}$

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

$x = \frac{14 \pm 22}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{14 \pm 22}{6}$

Simplify $\frac{14 \pm 22}{6}$ .

$x = \frac{7 \pm 11}{3}$

Step 5

The final answer is the combination of both solutions.

$x = 6, - \frac{4}{3}$