Solve Using the Quadratic Formula 3x^2-150=282

$3 x^{2} - 150 = 282$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $282$ from both sides of the equation.

$3 x^{2} - 150 - 282 = 0$

Subtract $282$ from $- 150$ .

$3 x^{2} - 432 = 0$

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 $a = 3$ , $b = 0$ , and $c = - 432$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 432)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 432}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 432$ .

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot - 432}}{2 \cdot 3}$

Multiply $- 12$ by $- 432$ .

$x = \frac{0 \pm \sqrt{0 + 5184}}{2 \cdot 3}$

Add $0$ and $5184$ .

$x = \frac{0 \pm \sqrt{5184}}{2 \cdot 3}$

Rewrite $5184$ as $72^{2}$ .

$x = \frac{0 \pm \sqrt{72^{2}}}{2 \cdot 3}$

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

$x = \frac{0 \pm 72}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{0 \pm 72}{6}$

Simplify $\frac{0 \pm 72}{6}$ .

$x = \pm 12$

Step 5

The final answer is the combination of both solutions.

$x = 12, - 12$