x+(x+110)(x+25)=180

Solution for x+(x+110)(x+25)=180 equation:

x+(x+110)(x+25)=180

We move all terms to the left:

x+(x+110)(x+25)-(180)=0

We multiply parentheses ..

(+x^2+25x+110x+2750)+x-180=0

We get rid of parentheses

x^2+25x+110x+x+2750-180=0

We add all the numbers together, and all the variables

x^2+136x+2570=0

a = 1; b = 136; c = +2570;
Δ = b2-4ac
Δ = 1362-4·1·2570
Δ = 8216
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:

$\sqrt{\Delta}=\sqrt{8216}=\sqrt{4*2054}=\sqrt{4}*\sqrt{2054}=2\sqrt{2054}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-2\sqrt{2054}}{2*1}=\frac{-136-2\sqrt{2054}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+2\sqrt{2054}}{2*1}=\frac{-136+2\sqrt{2054}}{2}
$