10/3m+4/m=4

Solution for 10/3m+4/m=4 equation:

10/3m+4/m=4

We move all terms to the left:

10/3m+4/m-(4)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: m!=0

m∈R


We calculate fractions


10m/3m^2+12m/3m^2-4=0

We multiply all the terms by the denominator


10m+12m-4*3m^2=0

We add all the numbers together, and all the variables

22m-4*3m^2=0

Wy multiply elements

-12m^2+22m=0

a = -12; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-12)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-12}=\frac{-44}{-24}
=1+5/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-12}=\frac{0}{-24}
=0
$