y^2-36y+72=0

Solution for y^2-36y+72=0 equation:

y^2-36y+72=0

a = 1; b = -36; c = +72;
Δ = b2-4ac
Δ = -362-4·1·72
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{7}}{2*1}=\frac{36-12\sqrt{7}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{7}}{2*1}=\frac{36+12\sqrt{7}}{2}
$