2y^2-36y-32=0

Solution for 2y^2-36y-32=0 equation:

2y^2-36y-32=0

a = 2; b = -36; c = -32;
Δ = b2-4ac
Δ = -362-4·2·(-32)
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{97}}{2*2}=\frac{36-4\sqrt{97}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{97}}{2*2}=\frac{36+4\sqrt{97}}{4}
$