(2x-7)(3x-12)=0

Solution for (2x-7)(3x-12)=0 equation:

(2x-7)(3x-12)=0

We multiply parentheses ..

(+6x^2-24x-21x+84)=0

We get rid of parentheses

6x^2-24x-21x+84=0

We add all the numbers together, and all the variables

6x^2-45x+84=0

a = 6; b = -45; c = +84;
Δ = b2-4ac
Δ = -452-4·6·84
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*6}=\frac{42}{12}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3}{2*6}=\frac{48}{12}
=4
$