(9x+1)(10x-11)=90

Solution for (9x+1)(10x-11)=90 equation:

(9x+1)(10x-11)=90

We move all terms to the left:

(9x+1)(10x-11)-(90)=0

We multiply parentheses ..

(+90x^2-99x+10x-11)-90=0

We get rid of parentheses

90x^2-99x+10x-11-90=0

We add all the numbers together, and all the variables

90x^2-89x-101=0

a = 90; b = -89; c = -101;
Δ = b2-4ac
Δ = -892-4·90·(-101)
Δ = 44281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-\sqrt{44281}}{2*90}=\frac{89-\sqrt{44281}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{44281}}{2*90}=\frac{89+\sqrt{44281}}{180}
$