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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+63x^2-81x+7x-9))+5x-1=0


We calculate terms in parentheses: -((+63x^2-81x+7x-9)), so:

(+63x^2-81x+7x-9)

We get rid of parentheses

63x^2-81x+7x-9

We add all the numbers together, and all the variables

63x^2-74x-9

Back to the equation:

-(63x^2-74x-9)


We add all the numbers together, and all the variables

5x-(63x^2-74x-9)-1=0

We get rid of parentheses

-63x^2+5x+74x+9-1=0

We add all the numbers together, and all the variables

-63x^2+79x+8=0

a = -63; b = 79; c = +8;
Δ = b2-4ac
Δ = 792-4·(-63)·8
Δ = 8257
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{8257}}{2*-63}=\frac{-79-\sqrt{8257}}{-126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+\sqrt{8257}}{2*-63}=\frac{-79+\sqrt{8257}}{-126}
$