x^2-50x-100=1500

Solution for x^2-50x-100=1500 equation:

x^2-50x-100=1500

We move all terms to the left:

x^2-50x-100-(1500)=0

We add all the numbers together, and all the variables

x^2-50x-1600=0

a = 1; b = -50; c = -1600;
Δ = b2-4ac
Δ = -502-4·1·(-1600)
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{89}}{2*1}=\frac{50-10\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{89}}{2*1}=\frac{50+10\sqrt{89}}{2}
$