# How do you solve 30x² + 5x - 10 = 0?

Aug 11, 2015

Solve $y = 30 {x}^{2} + 5 x - 10 = 0$ (1)

Ans: $\frac{1}{2} \mathmr{and} \left(- \frac{2}{3}\right)$

#### Explanation:

I use the new Transforming Method (Google, Yahoo Search).
Transformed equation: $y ' = {x}^{2} + 5 x - 300 = 0$ (2).
Roots have opposite signs (Rule of signs).
Factor pairs of (-300): ...(-10, 30)(-15, 20). This sum is 5 = b. Then the 2 real roots of (2) are the opposite: y1 = 15 and y2 = -20 .
Back to original equation (1), the 2 real roots are: $x 1 = \frac{y 1}{a} = \frac{15}{30} = \frac{1}{2}$, and $x 2 = \frac{y 2}{a} = - \frac{20}{30} = - \frac{2}{3}$

NOTE. This method avoid the lengthy factoring by grouping and solving the 2 binomials.