4x+x^2=180

Solution for 4x+x^2=180 equation:

4x+x^2=180

We move all terms to the left:

4x+x^2-(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}
$