(x^2+10x)+(2x+45)=180

Solution for (x^2+10x)+(2x+45)=180 equation:

(x^2+10x)+(2x+45)=180

We move all terms to the left:

(x^2+10x)+(2x+45)-(180)=0

We get rid of parentheses

x^2+10x+2x+45-180=0

We add all the numbers together, and all the variables

x^2+12x-135=0

a = 1; b = 12; c = -135;
Δ = b2-4ac
Δ = 122-4·1·(-135)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{19}}{2*1}=\frac{-12-6\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{19}}{2*1}=\frac{-12+6\sqrt{19}}{2}
$