2m+6=4/3m

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

2m+6=4/3m

We move all terms to the left:

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


Domain of the equation: 3m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2m-4/3m+6=0

We multiply all the terms by the denominator


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

Wy multiply elements

6m^2+18m-4=0

a = 6; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·6·(-4)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*6}=\frac{-18-2\sqrt{105}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*6}=\frac{-18+2\sqrt{105}}{12}
$