2(3x-8)(6x-7)=0

Solution for 2(3x-8)(6x-7)=0 equation:

2(3x-8)(6x-7)=0

We multiply parentheses ..

2(+18x^2-21x-48x+56)=0

We multiply parentheses

36x^2-42x-96x+112=0

We add all the numbers together, and all the variables

36x^2-138x+112=0

a = 36; b = -138; c = +112;
Δ = b2-4ac
Δ = -1382-4·36·112
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-54}{2*36}=\frac{84}{72}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+54}{2*36}=\frac{192}{72}
=2+2/3
$