x^2-85x+900=0

Solution for x^2-85x+900=0 equation:

x^2-85x+900=0

a = 1; b = -85; c = +900;
Δ = b2-4ac
Δ = -852-4·1·900
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-5\sqrt{145}}{2*1}=\frac{85-5\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+5\sqrt{145}}{2*1}=\frac{85+5\sqrt{145}}{2}
$