x2-90x+36=0

Solution for x2-90x+36=0 equation:

x2-90x+36=0

We add all the numbers together, and all the variables

x^2-90x+36=0

a = 1; b = -90; c = +36;
Δ = b2-4ac
Δ = -902-4·1·36
Δ = 7956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7956}=\sqrt{36*221}=\sqrt{36}*\sqrt{221}=6\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{221}}{2*1}=\frac{90-6\sqrt{221}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{221}}{2*1}=\frac{90+6\sqrt{221}}{2}
$