x^2-20x-101=0

Solution for x^2-20x-101=0 equation:

x^2-20x-101=0

a = 1; b = -20; c = -101;
Δ = b2-4ac
Δ = -202-4·1·(-101)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{201}}{2*1}=\frac{20-2\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{201}}{2*1}=\frac{20+2\sqrt{201}}{2}
$