(4x+18)(2x+36)=180

Solution for (4x+18)(2x+36)=180 equation:

(4x+18)(2x+36)=180

We move all terms to the left:

(4x+18)(2x+36)-(180)=0

We multiply parentheses ..

(+8x^2+144x+36x+648)-180=0

We get rid of parentheses

8x^2+144x+36x+648-180=0

We add all the numbers together, and all the variables

8x^2+180x+468=0

a = 8; b = 180; c = +468;
Δ = b2-4ac
Δ = 1802-4·8·468
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-132}{2*8}=\frac{-312}{16}
=-19+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+132}{2*8}=\frac{-48}{16}
=-3
$