0=2m^2+8m-32

Solution for 0=2m^2+8m-32 equation:

0=2m^2+8m-32

We move all terms to the left:

0-(2m^2+8m-32)=0

We add all the numbers together, and all the variables

-(2m^2+8m-32)=0

We get rid of parentheses

-2m^2-8m+32=0

a = -2; b = -8; c = +32;
Δ = b2-4ac
Δ = -82-4·(-2)·32
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{5}}{2*-2}=\frac{8-8\sqrt{5}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{5}}{2*-2}=\frac{8+8\sqrt{5}}{-4}
$