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

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

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

We multiply parentheses ..

2(+7m^2-8m-42m+48)=0

We multiply parentheses

14m^2-16m-84m+96=0

We add all the numbers together, and all the variables

14m^2-100m+96=0

a = 14; b = -100; c = +96;
Δ = b2-4ac
Δ = -1002-4·14·96
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-68}{2*14}=\frac{32}{28}
=1+1/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+68}{2*14}=\frac{168}{28}
=6
$