y^2-20y+90=0

Solution for y^2-20y+90=0 equation:

y^2-20y+90=0

a = 1; b = -20; c = +90;
Δ = b2-4ac
Δ = -202-4·1·90
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{10}}{2*1}=\frac{20-2\sqrt{10}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{10}}{2*1}=\frac{20+2\sqrt{10}}{2}
$