y^2+36y+90=0

Solution for y^2+36y+90=0 equation:

y^2+36y+90=0

a = 1; b = 36; c = +90;
Δ = b2-4ac
Δ = 362-4·1·90
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{26}}{2*1}=\frac{-36-6\sqrt{26}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{26}}{2*1}=\frac{-36+6\sqrt{26}}{2}
$