5-7/6m=3/2m+4

Solution for 5-7/6m=3/2m+4 equation:

5-7/6m=3/2m+4

We move all terms to the left:

5-7/6m-(3/2m+4)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 2m+4)!=0

m∈R


We get rid of parentheses

-7/6m-3/2m-4+5=0

We calculate fractions


(-14m)/12m^2+(-18m)/12m^2-4+5=0

We add all the numbers together, and all the variables

(-14m)/12m^2+(-18m)/12m^2+1=0

We multiply all the terms by the denominator


(-14m)+(-18m)+1*12m^2=0

Wy multiply elements

12m^2+(-14m)+(-18m)=0

We get rid of parentheses

12m^2-14m-18m=0

We add all the numbers together, and all the variables

12m^2-32m=0

a = 12; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·12·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*12}=\frac{0}{24}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*12}=\frac{64}{24}
=2+2/3
$