2y2-36y-144=0

Solution for 2y2-36y-144=0 equation:

2y^2-36y-144=0

a = 2; b = -36; c = -144;
Δ = b2-4ac
Δ = -362-4·2·(-144)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{17}}{2*2}=\frac{36-12\sqrt{17}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{17}}{2*2}=\frac{36+12\sqrt{17}}{4}
$