Solve Using the Quadratic Formula 3x^2+72=33x

$3 x^{2} + 72 = 33 x$

Step 1

Subtract $33 x$ from both sides of the equation.

$3 x^{2} + 72 - 33 x = 0$

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 $a = 3$ , $b = - 33$ , and $c = 72$ into the quadratic formula and solve for $x$ .

$\frac{33 \pm \sqrt{{(- 33)}^{2} - 4 \cdot (3 \cdot 72)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 33$ to the power of $2$ .

$x = \frac{33 \pm \sqrt{1089 - 4 \cdot 3 \cdot 72}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 72$ .

Multiply $- 4$ by $3$ .

$x = \frac{33 \pm \sqrt{1089 - 12 \cdot 72}}{2 \cdot 3}$

Multiply $- 12$ by $72$ .

$x = \frac{33 \pm \sqrt{1089 - 864}}{2 \cdot 3}$

Subtract $864$ from $1089$ .

$x = \frac{33 \pm \sqrt{225}}{2 \cdot 3}$

Rewrite $225$ as $15^{2}$ .

$x = \frac{33 \pm \sqrt{15^{2}}}{2 \cdot 3}$

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

$x = \frac{33 \pm 15}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{33 \pm 15}{6}$

Simplify $\frac{33 \pm 15}{6}$ .

$x = \frac{11 \pm 5}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 8, 3$