8+x^2=180

Solution for 8+x^2=180 equation:

8+x^2=180

We move all terms to the left:

8+x^2-(180)=0

We add all the numbers together, and all the variables

x^2-172=0

a = 1; b = 0; c = -172;
Δ = b2-4ac
Δ = 02-4·1·(-172)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{43}}{2*1}=\frac{0-4\sqrt{43}}{2}
=-\frac{4\sqrt{43}}{2}
=-2\sqrt{43}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{43}}{2*1}=\frac{0+4\sqrt{43}}{2}
=\frac{4\sqrt{43}}{2}
=2\sqrt{43}
$