x^2-90x+900=0

Solution for x^2-90x+900=0 equation:

x^2-90x+900=0

a = 1; b = -90; c = +900;
Δ = b2-4ac
Δ = -902-4·1·900
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{5}}{2*1}=\frac{90-30\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{5}}{2*1}=\frac{90+30\sqrt{5}}{2}
$