x^2+90x=150

Solution for x^2+90x=150 equation:

x^2+90x=150

We move all terms to the left:

x^2+90x-(150)=0

a = 1; b = 90; c = -150;
Δ = b2-4ac
Δ = 902-4·1·(-150)
Δ = 8700
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:

$\sqrt{\Delta}=\sqrt{8700}=\sqrt{100*87}=\sqrt{100}*\sqrt{87}=10\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{87}}{2*1}=\frac{-90-10\sqrt{87}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{87}}{2*1}=\frac{-90+10\sqrt{87}}{2}
$