(X+40)(2x+18)=180

Solution for (X+40)(2x+18)=180 equation:

(X+40)(2X+18)=180

We move all terms to the left:

(X+40)(2X+18)-(180)=0

We multiply parentheses ..

(+2X^2+18X+80X+720)-180=0

We get rid of parentheses

2X^2+18X+80X+720-180=0

We add all the numbers together, and all the variables

2X^2+98X+540=0

a = 2; b = 98; c = +540;
Δ = b2-4ac
Δ = 982-4·2·540
Δ = 5284
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:

$\sqrt{\Delta}=\sqrt{5284}=\sqrt{4*1321}=\sqrt{4}*\sqrt{1321}=2\sqrt{1321}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-2\sqrt{1321}}{2*2}=\frac{-98-2\sqrt{1321}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+2\sqrt{1321}}{2*2}=\frac{-98+2\sqrt{1321}}{4}
$