(7x-1)(9x=3)=(x+1)(3x-1)

Solution for (7x-1)(9x=3)=(x+1)(3x-1) equation:

(7x-1)(9x=3)=(x+1)(3x-1)

We move all terms to the left:

(7x-1)(9x-(3))=0

We multiply parentheses ..

(+63x^2-21x-9x+3)=0

We get rid of parentheses

63x^2-21x-9x+3=0

We add all the numbers together, and all the variables

63x^2-30x+3=0

a = 63; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·63·3
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12}{2*63}=\frac{18}{126}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12}{2*63}=\frac{42}{126}
=1/3
$