4/(m+2)+6=3m

Solution for 4/(m+2)+6=3m equation:

4/(m+2)+6=3m

We move all terms to the left:

4/(m+2)+6-(3m)=0


Domain of the equation: (m+2)!=0

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

m!=-2

m∈R


We add all the numbers together, and all the variables

-3m+4/(m+2)+6=0

We multiply all the terms by the denominator


-3m*(m+2)+6*(m+2)+4=0

We multiply parentheses

-3m^2-6m+6m+12+4=0

We add all the numbers together, and all the variables

-3m^2+16=0

a = -3; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-3)·16
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-3}=\frac{0-8\sqrt{3}}{-6}
=-\frac{8\sqrt{3}}{-6}
=-\frac{4\sqrt{3}}{-3}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-3}=\frac{0+8\sqrt{3}}{-6}
=\frac{8\sqrt{3}}{-6}
=\frac{4\sqrt{3}}{-3}
$