(9x+1)(7x-9)=(5x-11)

Solution for (9x+1)(7x-9)=(5x-11) equation:

(9x+1)(7x-9)=(5x-11)

We move all terms to the left:

(9x+1)(7x-9)-((5x-11))=0

We multiply parentheses ..

(+63x^2-81x+7x-9)-((5x-11))=0


We calculate terms in parentheses: -((5x-11)), so:

(5x-11)

We get rid of parentheses

5x-11

Back to the equation:

-(5x-11)


We get rid of parentheses

63x^2-81x+7x-5x-9+11=0

We add all the numbers together, and all the variables

63x^2-79x+2=0

a = 63; b = -79; c = +2;
Δ = b2-4ac
Δ = -792-4·63·2
Δ = 5737
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{-(-79)-\sqrt{5737}}{2*63}=\frac{79-\sqrt{5737}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{5737}}{2*63}=\frac{79+\sqrt{5737}}{126}
$