-15r^2-17r+42=0

Solution for -15r^2-17r+42=0 equation:

-15r^2-17r+42=0

a = -15; b = -17; c = +42;
Δ = b2-4ac
Δ = -172-4·(-15)·42
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-53}{2*-15}=\frac{-36}{-30}
=1+1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+53}{2*-15}=\frac{70}{-30}
=-2+1/3
$