x^2+90x=900

Solution for x^2+90x=900 equation:

x^2+90x=900

We move all terms to the left:

x^2+90x-(900)=0

a = 1; b = 90; c = -900;
Δ = b2-4ac
Δ = 902-4·1·(-900)
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-30\sqrt{13}}{2*1}=\frac{-90-30\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+30\sqrt{13}}{2*1}=\frac{-90+30\sqrt{13}}{2}
$