# How do you solve 2a^2-30a+108=0?

Jul 30, 2015

Solve $f \left(x\right) = 2 {a}^{2} - 30 a + 108 = 0$

Ans: 6 and 9

#### Explanation:

$f \left(x\right) = 2 y = 2 \left({a}^{2} - 15 a + 54\right) = 0$
$y = {a}^{2} - 15 a + 54 = 0$
I use the new Transforming Method. Both roots are positive.
Factor pairs of (54) -> (2, 27)(3, 18)(6, 9). This sum is 15 = -b.
Then, the 2 real roots of y are : 6 and 9

Use the Bhaskara formula to find $x ' = 9$ and $x ' ' = 6$.
The Bhaskara formula is: $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$, where a is the number that multiplies ${x}^{2}$, b is the number that multiplies $x$ and c is the number that doesn't multiply anyone. You should get to the following calculation:
$x = \frac{30 \pm 6}{4}$.