X^2+500x-7500=0

Solution for X^2+500x-7500=0 equation:

X^2+500X-7500=0

a = 1; b = 500; c = -7500;
Δ = b2-4ac
Δ = 5002-4·1·(-7500)
Δ = 280000
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:

$\sqrt{\Delta}=\sqrt{280000}=\sqrt{40000*7}=\sqrt{40000}*\sqrt{7}=200\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-200\sqrt{7}}{2*1}=\frac{-500-200\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+200\sqrt{7}}{2*1}=\frac{-500+200\sqrt{7}}{2}
$