x^2-850x-5000=0

Solution for x^2-850x-5000=0 equation:

x^2-850x-5000=0

a = 1; b = -850; c = -5000;
Δ = b2-4ac
Δ = -8502-4·1·(-5000)
Δ = 742500
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:

$\sqrt{\Delta}=\sqrt{742500}=\sqrt{22500*33}=\sqrt{22500}*\sqrt{33}=150\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-850)-150\sqrt{33}}{2*1}=\frac{850-150\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-850)+150\sqrt{33}}{2*1}=\frac{850+150\sqrt{33}}{2}
$