8-2m^2=m^2+5

Solution for 8-2m^2=m^2+5 equation:

8-2m^2=m^2+5

We move all terms to the left:

8-2m^2-(m^2+5)=0

We get rid of parentheses

-2m^2-m^2-5+8=0

We add all the numbers together, and all the variables

-3m^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$