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 = 10900
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:

$\sqrt{\Delta}=\sqrt{10900}=\sqrt{100*109}=\sqrt{100}*\sqrt{109}=10\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{109}}{2*1}=\frac{100-10\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{109}}{2*1}=\frac{100+10\sqrt{109}}{2}
$