42r^2-17r-15=0

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

42r^2-17r-15=0

a = 42; b = -17; c = -15;
Δ = b2-4ac
Δ = -172-4·42·(-15)
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*42}=\frac{-36}{84}
=-3/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+53}{2*42}=\frac{70}{84}
=5/6
$