(9x+3)(11x-21)=(5x-2)

Solution for (9x+3)(11x-21)=(5x-2) equation:

(9x+3)(11x-21)=(5x-2)

We move all terms to the left:

(9x+3)(11x-21)-((5x-2))=0

We multiply parentheses ..

(+99x^2-189x+33x-63)-((5x-2))=0


We calculate terms in parentheses: -((5x-2)), so:

(5x-2)

We get rid of parentheses

5x-2

Back to the equation:

-(5x-2)


We get rid of parentheses

99x^2-189x+33x-5x-63+2=0

We add all the numbers together, and all the variables

99x^2-161x-61=0

a = 99; b = -161; c = -61;
Δ = b2-4ac
Δ = -1612-4·99·(-61)
Δ = 50077
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{-(-161)-\sqrt{50077}}{2*99}=\frac{161-\sqrt{50077}}{198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-161)+\sqrt{50077}}{2*99}=\frac{161+\sqrt{50077}}{198}
$