(3x-4)(9x-7)=0

Solution for (3x-4)(9x-7)=0 equation:

(3x-4)(9x-7)=0

We multiply parentheses ..

(+27x^2-21x-36x+28)=0

We get rid of parentheses

27x^2-21x-36x+28=0

We add all the numbers together, and all the variables

27x^2-57x+28=0

a = 27; b = -57; c = +28;
Δ = b2-4ac
Δ = -572-4·27·28
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-15}{2*27}=\frac{42}{54}
=7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+15}{2*27}=\frac{72}{54}
=1+1/3
$