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

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

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

We multiply parentheses ..

(+12x^2-21x-16x+28)=0

We get rid of parentheses

12x^2-21x-16x+28=0

We add all the numbers together, and all the variables

12x^2-37x+28=0

a = 12; b = -37; c = +28;
Δ = b2-4ac
Δ = -372-4·12·28
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-5}{2*12}=\frac{32}{24}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+5}{2*12}=\frac{42}{24}
=1+3/4
$