x(x+12)+100=180

Solution for x(x+12)+100=180 equation:

x(x+12)+100=180

We move all terms to the left:

x(x+12)+100-(180)=0

We add all the numbers together, and all the variables

x(x+12)-80=0

We multiply parentheses

x^2+12x-80=0

a = 1; b = 12; c = -80;
Δ = b2-4ac
Δ = 122-4·1·(-80)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{29}}{2*1}=\frac{-12-4\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{29}}{2*1}=\frac{-12+4\sqrt{29}}{2}
$