x^2+50x+80=180

Solution for x^2+50x+80=180 equation:

x^2+50x+80=180

We move all terms to the left:

x^2+50x+80-(180)=0

We add all the numbers together, and all the variables

x^2+50x-100=0

a = 1; b = 50; c = -100;
Δ = b2-4ac
Δ = 502-4·1·(-100)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{29}}{2*1}=\frac{-50-10\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{29}}{2*1}=\frac{-50+10\sqrt{29}}{2}
$