(6x-7)(9x-1)=0.

Solution for (6x-7)(9x-1)=0. equation:

(6x-7)(9x-1)=0.

We multiply parentheses ..

(+54x^2-6x-63x+7)=0

We get rid of parentheses

54x^2-6x-63x+7=0

We add all the numbers together, and all the variables

54x^2-69x+7=0

a = 54; b = -69; c = +7;
Δ = b2-4ac
Δ = -692-4·54·7
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-57}{2*54}=\frac{12}{108}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+57}{2*54}=\frac{126}{108}
=1+1/6
$