2y^2-24y+36=0

Solution for 2y^2-24y+36=0 equation:

2y^2-24y+36=0

a = 2; b = -24; c = +36;
Δ = b2-4ac
Δ = -242-4·2·36
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{2}}{2*2}=\frac{24-12\sqrt{2}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{2}}{2*2}=\frac{24+12\sqrt{2}}{4}
$