x+x^2+x^2=180

Solution for x+x^2+x^2=180 equation:

x+x^2+x^2=180

We move all terms to the left:

x+x^2+x^2-(180)=0

We add all the numbers together, and all the variables

2x^2+x-180=0

a = 2; b = 1; c = -180;
Δ = b2-4ac
Δ = 12-4·2·(-180)
Δ = 1441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1441}}{2*2}=\frac{-1-\sqrt{1441}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1441}}{2*2}=\frac{-1+\sqrt{1441}}{4}
$