9x+27+x^2-6x=180

Solution for 9x+27+x^2-6x=180 equation:

9x+27+x^2-6x=180

We move all terms to the left:

9x+27+x^2-6x-(180)=0

We add all the numbers together, and all the variables

x^2+3x-153=0

a = 1; b = 3; c = -153;
Δ = b2-4ac
Δ = 32-4·1·(-153)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{69}}{2*1}=\frac{-3-3\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{69}}{2*1}=\frac{-3+3\sqrt{69}}{2}
$