(2x-7)(6x-8)=0

Solution for (2x-7)(6x-8)=0 equation:

(2x-7)(6x-8)=0

We multiply parentheses ..

(+12x^2-16x-42x+56)=0

We get rid of parentheses

12x^2-16x-42x+56=0

We add all the numbers together, and all the variables

12x^2-58x+56=0

a = 12; b = -58; c = +56;
Δ = b2-4ac
Δ = -582-4·12·56
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-26}{2*12}=\frac{32}{24}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+26}{2*12}=\frac{84}{24}
=3+1/2
$