5m^2+8m=-1

Solution for 5m^2+8m=-1 equation:

5m^2+8m=-1

We move all terms to the left:

5m^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 = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{11}}{2*5}=\frac{-8-2\sqrt{11}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{11}}{2*5}=\frac{-8+2\sqrt{11}}{10}
$