2x+x^2=90

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

2x+x^2=90

We move all terms to the left:

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

a = 1; b = 2; c = -90;
Δ = b2-4ac
Δ = 22-4·1·(-90)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*1}=\frac{-2-2\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*1}=\frac{-2+2\sqrt{91}}{2}
$