7x+16+x^2+x=180

Solution for 7x+16+x^2+x=180 equation:

7x+16+x^2+x=180

We move all terms to the left:

7x+16+x^2+x-(180)=0

We add all the numbers together, and all the variables

x^2+8x-164=0

a = 1; b = 8; c = -164;
Δ = b2-4ac
Δ = 82-4·1·(-164)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{5}}{2*1}=\frac{-8-12\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{5}}{2*1}=\frac{-8+12\sqrt{5}}{2}
$