9-2x+x^2=180

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

9-2x+x^2=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2-2x-171=0

a = 1; b = -2; c = -171;
Δ = b2-4ac
Δ = -22-4·1·(-171)
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{-(-2)-4\sqrt{43}}{2*1}=\frac{2-4\sqrt{43}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{43}}{2*1}=\frac{2+4\sqrt{43}}{2}
$