x2+(-2x)2=180

Solution for x2+(-2x)2=180 equation:

x2+(-2x)2=180

We move all terms to the left:

x2+(-2x)2-(180)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-4x-180=0

a = 1; b = -4; c = -180;
Δ = b2-4ac
Δ = -42-4·1·(-180)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*1}=\frac{4-4\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*1}=\frac{4+4\sqrt{46}}{2}
$