(2x-8)(3x-7)=0

Solution for (2x-8)(3x-7)=0 equation:

(2x-8)(3x-7)=0

We multiply parentheses ..

(+6x^2-14x-24x+56)=0

We get rid of parentheses

6x^2-14x-24x+56=0

We add all the numbers together, and all the variables

6x^2-38x+56=0

a = 6; b = -38; c = +56;
Δ = b2-4ac
Δ = -382-4·6·56
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-10}{2*6}=\frac{28}{12}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+10}{2*6}=\frac{48}{12}
=4
$