x^2-100x+225=0

Solution for x^2-100x+225=0 equation:

x^2-100x+225=0

a = 1; b = -100; c = +225;
Δ = b2-4ac
Δ = -1002-4·1·225
Δ = 9100
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:

$\sqrt{\Delta}=\sqrt{9100}=\sqrt{100*91}=\sqrt{100}*\sqrt{91}=10\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{91}}{2*1}=\frac{100-10\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{91}}{2*1}=\frac{100+10\sqrt{91}}{2}
$