5m^2=-6-31m

Solution for 5m^2=-6-31m equation:

5m^2=-6-31m

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5m^2+31m+6=0

a = 5; b = 31; c = +6;
Δ = b2-4ac
Δ = 312-4·5·6
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*5}=\frac{-60}{10}
=-6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+29}{2*5}=\frac{-2}{10}
=-1/5
$