m^2+5m+1m=-2

Solution for m^2+5m+1m=-2 equation:

m^2+5m+1m=-2

We move all terms to the left:

m^2+5m+1m-(-2)=0

We add all the numbers together, and all the variables

m^2+6m+2=0

a = 1; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·1·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*1}=\frac{-6-2\sqrt{7}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*1}=\frac{-6+2\sqrt{7}}{2}
$