x^2-100x-50=0

Solution for x^2-100x-50=0 equation:

X^2-100X-50=0

a = 1; b = -100; c = -50;
Δ = b2-4ac
Δ = -1002-4·1·(-50)
Δ = 10200
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:

$\sqrt{\Delta}=\sqrt{10200}=\sqrt{100*102}=\sqrt{100}*\sqrt{102}=10\sqrt{102}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{102}}{2*1}=\frac{100-10\sqrt{102}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{102}}{2*1}=\frac{100+10\sqrt{102}}{2}
$