x^2+150x-2000=0

Solution for x^2+150x-2000=0 equation:

x^2+150x-2000=0

a = 1; b = 150; c = -2000;
Δ = b2-4ac
Δ = 1502-4·1·(-2000)
Δ = 30500
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:

$\sqrt{\Delta}=\sqrt{30500}=\sqrt{100*305}=\sqrt{100}*\sqrt{305}=10\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{305}}{2*1}=\frac{-150-10\sqrt{305}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{305}}{2*1}=\frac{-150+10\sqrt{305}}{2}
$