4m^2+8m-1=-m^2

Solution for 4m^2+8m-1=-m^2 equation:

4m^2+8m-1=-m^2

We move all terms to the left:

4m^2+8m-1-(-m^2)=0

We get rid of parentheses

4m^2+m^2+8m-1=0

We add all the numbers together, and all the variables

5m^2+8m-1=0

a = 5; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·5·(-1)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{21}}{2*5}=\frac{-8-2\sqrt{21}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{21}}{2*5}=\frac{-8+2\sqrt{21}}{10}
$