36r^2-120r+36=0

Solution for 36r^2-120r+36=0 equation:

36r^2-120r+36=0

a = 36; b = -120; c = +36;
Δ = b2-4ac
Δ = -1202-4·36·36
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-96}{2*36}=\frac{24}{72}
=1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+96}{2*36}=\frac{216}{72}
=3
$