(9x+18)(10x-8)=180

Solution for (9x+18)(10x-8)=180 equation:

(9x+18)(10x-8)=180

We move all terms to the left:

(9x+18)(10x-8)-(180)=0

We multiply parentheses ..

(+90x^2-72x+180x-144)-180=0

We get rid of parentheses

90x^2-72x+180x-144-180=0

We add all the numbers together, and all the variables

90x^2+108x-324=0

a = 90; b = 108; c = -324;
Δ = b2-4ac
Δ = 1082-4·90·(-324)
Δ = 128304
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:

$\sqrt{\Delta}=\sqrt{128304}=\sqrt{11664*11}=\sqrt{11664}*\sqrt{11}=108\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108\sqrt{11}}{2*90}=\frac{-108-108\sqrt{11}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108\sqrt{11}}{2*90}=\frac{-108+108\sqrt{11}}{180}
$