x^2+10+6x+50=180

Solution for x^2+10+6x+50=180 equation:

x^2+10+6x+50=180

We move all terms to the left:

x^2+10+6x+50-(180)=0

We add all the numbers together, and all the variables

x^2+6x-120=0

a = 1; b = 6; c = -120;
Δ = b2-4ac
Δ = 62-4·1·(-120)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{129}}{2*1}=\frac{-6-2\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{129}}{2*1}=\frac{-6+2\sqrt{129}}{2}
$