x^2+150x-250000=0

Solution for x^2+150x-250000=0 equation:

x^2+150x-250000=0

a = 1; b = 150; c = -250000;
Δ = b2-4ac
Δ = 1502-4·1·(-250000)
Δ = 1022500
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:

$\sqrt{\Delta}=\sqrt{1022500}=\sqrt{2500*409}=\sqrt{2500}*\sqrt{409}=50\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-50\sqrt{409}}{2*1}=\frac{-150-50\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+50\sqrt{409}}{2*1}=\frac{-150+50\sqrt{409}}{2}
$