(10x+1)(9x-11)=180

Solution for (10x+1)(9x-11)=180 equation:

(10x+1)(9x-11)=180

We move all terms to the left:

(10x+1)(9x-11)-(180)=0

We multiply parentheses ..

(+90x^2-110x+9x-11)-180=0

We get rid of parentheses

90x^2-110x+9x-11-180=0

We add all the numbers together, and all the variables

90x^2-101x-191=0

a = 90; b = -101; c = -191;
Δ = b2-4ac
Δ = -1012-4·90·(-191)
Δ = 78961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78961}=281$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-281}{2*90}=\frac{-180}{180}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+281}{2*90}=\frac{382}{180}
=2+11/90
$