Solve Using the Quadratic Formula 2a^2-30a+108=0

$2 a^{2} - 30 a + 108 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 2$ , $b = - 30$ , and $c = 108$ into the quadratic formula and solve for $a$ .

$\frac{30 \pm \sqrt{{(- 30)}^{2} - 4 \cdot (2 \cdot 108)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 30$ to the power of $2$ .

$a = \frac{30 \pm \sqrt{900 - 4 \cdot 2 \cdot 108}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 108$ .

Multiply $- 4$ by $2$ .

$a = \frac{30 \pm \sqrt{900 - 8 \cdot 108}}{2 \cdot 2}$

Multiply $- 8$ by $108$ .

$a = \frac{30 \pm \sqrt{900 - 864}}{2 \cdot 2}$

Subtract $864$ from $900$ .

$a = \frac{30 \pm \sqrt{36}}{2 \cdot 2}$

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

$a = \frac{30 \pm \sqrt{6^{2}}}{2 \cdot 2}$

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

$a = \frac{30 \pm 6}{2 \cdot 2}$

Multiply $2$ by $2$ .

$a = \frac{30 \pm 6}{4}$

Simplify $\frac{30 \pm 6}{4}$ .

$a = \frac{15 \pm 3}{2}$

Step 4

The final answer is the combination of both solutions.

$a = 9, 6$