(x^2+8x)+(15x+40)=180

Solution for (x^2+8x)+(15x+40)=180 equation:

(x^2+8x)+(15x+40)=180

We move all terms to the left:

(x^2+8x)+(15x+40)-(180)=0

We get rid of parentheses

x^2+8x+15x+40-180=0

We add all the numbers together, and all the variables

x^2+23x-140=0

a = 1; b = 23; c = -140;
Δ = b2-4ac
Δ = 232-4·1·(-140)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-33}{2*1}=\frac{-56}{2}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+33}{2*1}=\frac{10}{2}
=5
$