3m+m+2/3m=28

Solution for 3m+m+2/3m=28 equation:

3m+m+2/3m=28

We move all terms to the left:

3m+m+2/3m-(28)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

4m+2/3m-28=0

We multiply all the terms by the denominator


4m*3m-28*3m+2=0

Wy multiply elements

12m^2-84m+2=0

a = 12; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·12·2
Δ = 6960
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:

$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{435}}{2*12}=\frac{84-4\sqrt{435}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{435}}{2*12}=\frac{84+4\sqrt{435}}{24}
$