6m2=-5+31m

Solution for 6m2=-5+31m equation:

6m^2=-5+31m

We move all terms to the left:

6m^2-(-5+31m)=0

We add all the numbers together, and all the variables

6m^2-(31m-5)=0

We get rid of parentheses

6m^2-31m+5=0

a = 6; b = -31; c = +5;
Δ = b2-4ac
Δ = -312-4·6·5
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-29}{2*6}=\frac{2}{12}
=1/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+29}{2*6}=\frac{60}{12}
=5
$