x^2-101x-500=0

Solution for x^2-101x-500=0 equation:

x^2-101x-500=0

a = 1; b = -101; c = -500;
Δ = b2-4ac
Δ = -1012-4·1·(-500)
Δ = 12201
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:

$\sqrt{\Delta}=\sqrt{12201}=\sqrt{49*249}=\sqrt{49}*\sqrt{249}=7\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-7\sqrt{249}}{2*1}=\frac{101-7\sqrt{249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+7\sqrt{249}}{2*1}=\frac{101+7\sqrt{249}}{2}
$