x(x+150)=500

Solution for x(x+150)=500 equation:

x(x+150)=500

We move all terms to the left:

x(x+150)-(500)=0

We multiply parentheses

x^2+150x-500=0

a = 1; b = 150; c = -500;
Δ = b2-4ac
Δ = 1502-4·1·(-500)
Δ = 24500
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:

$\sqrt{\Delta}=\sqrt{24500}=\sqrt{4900*5}=\sqrt{4900}*\sqrt{5}=70\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-70\sqrt{5}}{2*1}=\frac{-150-70\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+70\sqrt{5}}{2*1}=\frac{-150+70\sqrt{5}}{2}
$