7m^2=20+31m

Solution for 7m^2=20+31m equation:

7m^2=20+31m

We move all terms to the left:

7m^2-(20+31m)=0

We add all the numbers together, and all the variables

7m^2-(31m+20)=0

We get rid of parentheses

7m^2-31m-20=0

a = 7; b = -31; c = -20;
Δ = b2-4ac
Δ = -312-4·7·(-20)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-39}{2*7}=\frac{-8}{14}
=-4/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+39}{2*7}=\frac{70}{14}
=5
$