x(x+65)=180

Solution for x(x+65)=180 equation:

x(x+65)=180

We move all terms to the left:

x(x+65)-(180)=0

We multiply parentheses

x^2+65x-180=0

a = 1; b = 65; c = -180;
Δ = b2-4ac
Δ = 652-4·1·(-180)
Δ = 4945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-\sqrt{4945}}{2*1}=\frac{-65-\sqrt{4945}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4945}}{2*1}=\frac{-65+\sqrt{4945}}{2}
$