2(4x+26)+x^2=180

Solution for 2(4x+26)+x^2=180 equation:

2(4x+26)+x^2=180

We move all terms to the left:

2(4x+26)+x^2-(180)=0

We multiply parentheses

x^2+8x+52-180=0

We add all the numbers together, and all the variables

x^2+8x-128=0

a = 1; b = 8; c = -128;
Δ = b2-4ac
Δ = 82-4·1·(-128)
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{-(8)-24}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*1}=\frac{16}{2}
=8
$