(4x-7)(3x-6)=0

Solution for (4x-7)(3x-6)=0 equation:

(4x-7)(3x-6)=0

We multiply parentheses ..

(+12x^2-24x-21x+42)=0

We get rid of parentheses

12x^2-24x-21x+42=0

We add all the numbers together, and all the variables

12x^2-45x+42=0

a = 12; b = -45; c = +42;
Δ = b2-4ac
Δ = -452-4·12·42
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3}{2*12}=\frac{42}{24}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3}{2*12}=\frac{48}{24}
=2
$