x^2+500x-750000=0

Solution for x^2+500x-750000=0 equation:

x^2+500x-750000=0

a = 1; b = 500; c = -750000;
Δ = b2-4ac
Δ = 5002-4·1·(-750000)
Δ = 3250000
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:

$\sqrt{\Delta}=\sqrt{3250000}=\sqrt{250000*13}=\sqrt{250000}*\sqrt{13}=500\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-500\sqrt{13}}{2*1}=\frac{-500-500\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+500\sqrt{13}}{2*1}=\frac{-500+500\sqrt{13}}{2}
$