(x^2+5x)+(11x+27)=180

Solution for (x^2+5x)+(11x+27)=180 equation:

(x^2+5x)+(11x+27)=180

We move all terms to the left:

(x^2+5x)+(11x+27)-(180)=0

We get rid of parentheses

x^2+5x+11x+27-180=0

We add all the numbers together, and all the variables

x^2+16x-153=0

a = 1; b = 16; c = -153;
Δ = b2-4ac
Δ = 162-4·1·(-153)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{217}}{2*1}=\frac{-16-2\sqrt{217}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{217}}{2*1}=\frac{-16+2\sqrt{217}}{2}
$