9x+180=x^2

Solution for 9x+180=x^2 equation:

9x+180=x^2

We move all terms to the left:

9x+180-(x^2)=0

determiningTheFunctionDomain
-x^2+9x+180=0

We add all the numbers together, and all the variables

-1x^2+9x+180=0

a = -1; b = 9; c = +180;
Δ = b2-4ac
Δ = 92-4·(-1)·180
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{89}}{2*-1}=\frac{-9-3\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{89}}{2*-1}=\frac{-9+3\sqrt{89}}{-2}
$