(7x-9)(9x-13)=0

Solution for (7x-9)(9x-13)=0 equation:

(7x-9)(9x-13)=0

We multiply parentheses ..

(+63x^2-91x-81x+117)=0

We get rid of parentheses

63x^2-91x-81x+117=0

We add all the numbers together, and all the variables

63x^2-172x+117=0

a = 63; b = -172; c = +117;
Δ = b2-4ac
Δ = -1722-4·63·117
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-10}{2*63}=\frac{162}{126}
=1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+10}{2*63}=\frac{182}{126}
=1+4/9
$