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

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

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

We multiply parentheses

4m^2-12m-16=0

a = 4; b = -12; c = -16;
Δ = b2-4ac
Δ = -122-4·4·(-16)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*4}=\frac{-8}{8}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*4}=\frac{32}{8}
=4
$