x2+250x-562500=0

Solution for x2+250x-562500=0 equation:

x2+250x-562500=0

We add all the numbers together, and all the variables

x^2+250x-562500=0

a = 1; b = 250; c = -562500;
Δ = b2-4ac
Δ = 2502-4·1·(-562500)
Δ = 2312500
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:

$\sqrt{\Delta}=\sqrt{2312500}=\sqrt{62500*37}=\sqrt{62500}*\sqrt{37}=250\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-250\sqrt{37}}{2*1}=\frac{-250-250\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+250\sqrt{37}}{2*1}=\frac{-250+250\sqrt{37}}{2}
$