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

Solution for (7x+1)(9x-1)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

63x^2-7x+9x-1=0

We add all the numbers together, and all the variables

63x^2+2x-1=0

a = 63; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·63·(-1)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*63}=\frac{-18}{126}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*63}=\frac{14}{126}
=1/9
$