1+m^2+5m=-1

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

1+m^2+5m=-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

m^2+5m+2=0

a = 1; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·1·2
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{17}}{2*1}=\frac{-5-\sqrt{17}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{17}}{2*1}=\frac{-5+\sqrt{17}}{2}
$