# How do you solve 3x^2 + 19x -14 = 0?

Aug 11, 2015

Solve $y = 3 {x}^{2} + 19 x - 14 = 0$(1)

Ans: $\frac{2}{3}$ and -7.

#### Explanation:

I use the new Transforming Method (Google, Yahoo)
Transformed equation: $y ' = {x}^{2} + 19 x - 52 = 0$ (2) Roots have opposite signs (Rule of Signs).
Factor pairs of (-42) --> (-2, 21). This sum is 19 = b. Then the 2 real roots of (2) are the opposite. They are: y1 = 2 and y2 = - 21.
Back to original equation (1). The 2 real roots are: $x 1 = \frac{y 1}{a} = \frac{2}{3}$, and $x 2 = \frac{y 2}{a} = - \frac{21}{3} = - 7.$