x^2+16x+100=180

Solution for x^2+16x+100=180 equation:

x^2+16x+100=180

We move all terms to the left:

x^2+16x+100-(180)=0

We add all the numbers together, and all the variables

x^2+16x-80=0

a = 1; b = 16; c = -80;
Δ = b2-4ac
Δ = 162-4·1·(-80)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*1}=\frac{8}{2}
=4
$