X^2+250x-12500=0

Solution for X^2+250x-12500=0 equation:

X^2+250X-12500=0

a = 1; b = 250; c = -12500;
Δ = b2-4ac
Δ = 2502-4·1·(-12500)
Δ = 112500
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:

$\sqrt{\Delta}=\sqrt{112500}=\sqrt{22500*5}=\sqrt{22500}*\sqrt{5}=150\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-150\sqrt{5}}{2*1}=\frac{-250-150\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+150\sqrt{5}}{2*1}=\frac{-250+150\sqrt{5}}{2}
$