x2+250x+12500=0

Solution for x2+250x+12500=0 equation:

x2+250x+12500=0

We add all the numbers together, and all the variables

x^2+250x+12500=0

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

$\sqrt{\Delta}=\sqrt{12500}=\sqrt{2500*5}=\sqrt{2500}*\sqrt{5}=50\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-50\sqrt{5}}{2*1}=\frac{-250-50\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+50\sqrt{5}}{2*1}=\frac{-250+50\sqrt{5}}{2}
$