2/(m+1)=3m

Solution for 2/(m+1)=3m equation:

2/(m+1)=3m

We move all terms to the left:

2/(m+1)-(3m)=0


Domain of the equation: (m+1)!=0

We move all terms containing m to the left, all other terms to the right

m!=-1

m∈R


We add all the numbers together, and all the variables

-3m+2/(m+1)=0

We multiply all the terms by the denominator


-3m*(m+1)+2=0

We multiply parentheses

-3m^2-3m+2=0

a = -3; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-3)·2
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{33}}{2*-3}=\frac{3-\sqrt{33}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*-3}=\frac{3+\sqrt{33}}{-6}
$