(9x+21)(11x-1)=180

Solution for (9x+21)(11x-1)=180 equation:

(9x+21)(11x-1)=180

We move all terms to the left:

(9x+21)(11x-1)-(180)=0

We multiply parentheses ..

(+99x^2-9x+231x-21)-180=0

We get rid of parentheses

99x^2-9x+231x-21-180=0

We add all the numbers together, and all the variables

99x^2+222x-201=0

a = 99; b = 222; c = -201;
Δ = b2-4ac
Δ = 2222-4·99·(-201)
Δ = 128880
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:

$\sqrt{\Delta}=\sqrt{128880}=\sqrt{144*895}=\sqrt{144}*\sqrt{895}=12\sqrt{895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(222)-12\sqrt{895}}{2*99}=\frac{-222-12\sqrt{895}}{198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(222)+12\sqrt{895}}{2*99}=\frac{-222+12\sqrt{895}}{198}
$