x+(x+40)+x(x+65)=180

Solution for x+(x+40)+x(x+65)=180 equation:

x+(x+40)+x(x+65)=180

We move all terms to the left:

x+(x+40)+x(x+65)-(180)=0

We multiply parentheses

x^2+x+(x+40)+65x-180=0

We get rid of parentheses

x^2+x+x+65x+40-180=0

We add all the numbers together, and all the variables

x^2+67x-140=0

a = 1; b = 67; c = -140;
Δ = b2-4ac
Δ = 672-4·1·(-140)
Δ = 5049
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:

$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-3\sqrt{561}}{2*1}=\frac{-67-3\sqrt{561}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+3\sqrt{561}}{2*1}=\frac{-67+3\sqrt{561}}{2}
$