x2+250x-36500=0

Solution for x2+250x-36500=0 equation:

x2+250x-36500=0

We add all the numbers together, and all the variables

x^2+250x-36500=0

a = 1; b = 250; c = -36500;
Δ = b2-4ac
Δ = 2502-4·1·(-36500)
Δ = 208500
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:

$\sqrt{\Delta}=\sqrt{208500}=\sqrt{100*2085}=\sqrt{100}*\sqrt{2085}=10\sqrt{2085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{2085}}{2*1}=\frac{-250-10\sqrt{2085}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{2085}}{2*1}=\frac{-250+10\sqrt{2085}}{2}
$