Solve Using the Quadratic Formula 3x^2+45=24x

$3 x^{2} + 45 = 24 x$

Step 1

Subtract $24 x$ from both sides of the equation.

$3 x^{2} + 45 - 24 x = 0$

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 $a = 3$ , $b = - 24$ , and $c = 45$ into the quadratic formula and solve for $x$ .

$\frac{24 \pm \sqrt{{(- 24)}^{2} - 4 \cdot (3 \cdot 45)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 24$ to the power of $2$ .

$x = \frac{24 \pm \sqrt{576 - 4 \cdot 3 \cdot 45}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 45$ .

Multiply $- 4$ by $3$ .

$x = \frac{24 \pm \sqrt{576 - 12 \cdot 45}}{2 \cdot 3}$

Multiply $- 12$ by $45$ .

$x = \frac{24 \pm \sqrt{576 - 540}}{2 \cdot 3}$

Subtract $540$ from $576$ .

$x = \frac{24 \pm \sqrt{36}}{2 \cdot 3}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{24 \pm \sqrt{6^{2}}}{2 \cdot 3}$

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

$x = \frac{24 \pm 6}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{24 \pm 6}{6}$

Simplify $\frac{24 \pm 6}{6}$ .

$x = 4 \pm 1$

Step 5

The final answer is the combination of both solutions.

$x = 5, 3$