x(x-11)+73=180

Solution for x(x-11)+73=180 equation:

x(x-11)+73=180

We move all terms to the left:

x(x-11)+73-(180)=0

We add all the numbers together, and all the variables

x(x-11)-107=0

We multiply parentheses

x^2-11x-107=0

a = 1; b = -11; c = -107;
Δ = b2-4ac
Δ = -112-4·1·(-107)
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{61}}{2*1}=\frac{11-3\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{61}}{2*1}=\frac{11+3\sqrt{61}}{2}
$