x(x+27)=180

Solution for x(x+27)=180 equation:

x(x+27)=180

We move all terms to the left:

x(x+27)-(180)=0

We multiply parentheses

x^2+27x-180=0

a = 1; b = 27; c = -180;
Δ = b2-4ac
Δ = 272-4·1·(-180)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{161}}{2*1}=\frac{-27-3\sqrt{161}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{161}}{2*1}=\frac{-27+3\sqrt{161}}{2}
$