2m^2-52m=-82

Solution for 2m^2-52m=-82 equation:

2m^2-52m=-82

We move all terms to the left:

2m^2-52m-(-82)=0

We add all the numbers together, and all the variables

2m^2-52m+82=0

a = 2; b = -52; c = +82;
Δ = b2-4ac
Δ = -522-4·2·82
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-32\sqrt{2}}{2*2}=\frac{52-32\sqrt{2}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+32\sqrt{2}}{2*2}=\frac{52+32\sqrt{2}}{4}
$