6m=8-5m^2

Solution for 6m=8-5m^2 equation:

6m=8-5m^2

We move all terms to the left:

6m-(8-5m^2)=0

We get rid of parentheses

5m^2+6m-8=0

a = 5; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·5·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*5}=\frac{-20}{10}
=-2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*5}=\frac{8}{10}
=4/5
$