# How do you solve 6m^2 = 13m + 28?

Jun 28, 2015

Solve $y = 6 {x}^{2} - 13 x - 28 = 0$ (1)

#### Explanation:

I use the new Transforming Method (see Google or Yahoo Search).
Transformed equation: $y ' = {x}^{2} - 13 x - 168 = 0$ (2). Roots have different signs (Rule of signs).
Factor pairs of (ac = - 168) -> (6, 28)(-8, 21). This sum is 13 = -b.
The 2 real roots of (2) are: X1 = -8 and X2 = 21.

Back to original equation (1), the 2 real roots are:

$x 1 = X \frac{1}{a} = - \frac{8}{6} = - \frac{4}{3}$ and $x 2 = X \frac{2}{a} = \frac{21}{6} = \frac{7}{2}$