# How do you solve 4x^2 - 17x - 15 = 0 by factoring?

Solve $f \left(x\right) = 4 {x}^{2} - 17 x - 15 = 0$
Ans: $- \frac{3}{4}$ and 5
Transformed equation: $f \left(x\right) ' = {x}^{2} - 17 x - 60$. (2) Roots have opposite signs. Factor pairs of (-60) --> (-2, 30)(-3, 20). This sum is 17 = -b. Then, the 2 real roots of (2) are: y1 = -3 and y2 = 20.
Back to original equation, the 2 real roots are: $x 1 = \frac{y 1}{a} = - \frac{3}{4}$ and $x 2 = \frac{y 2}{a} = \frac{20}{4} = 5$.