20x^2-108x+36=0

Solution for 20x^2-108x+36=0 equation:

20x^2-108x+36=0

a = 20; b = -108; c = +36;
Δ = b2-4ac
Δ = -1082-4·20·36
Δ = 8784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-12\sqrt{61}}{2*20}=\frac{108-12\sqrt{61}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+12\sqrt{61}}{2*20}=\frac{108+12\sqrt{61}}{40}
$