180=9+x^2

Solution for 180=9+x^2 equation:

180=9+x^2

We move all terms to the left:

180-(9+x^2)=0

We get rid of parentheses

-x^2-9+180=0

We add all the numbers together, and all the variables

-1x^2+171=0

a = -1; b = 0; c = +171;
Δ = b2-4ac
Δ = 02-4·(-1)·171
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*-1}=\frac{0-6\sqrt{19}}{-2}
=-\frac{6\sqrt{19}}{-2}
=-\frac{3\sqrt{19}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*-1}=\frac{0+6\sqrt{19}}{-2}
=\frac{6\sqrt{19}}{-2}
=\frac{3\sqrt{19}}{-1}
$