5x+120+x^2+6x=180

Solution for 5x+120+x^2+6x=180 equation:

5x+120+x^2+6x=180

We move all terms to the left:

5x+120+x^2+6x-(180)=0

We add all the numbers together, and all the variables

x^2+11x-60=0

a = 1; b = 11; c = -60;
Δ = b2-4ac
Δ = 112-4·1·(-60)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*1}=\frac{8}{2}
=4
$