5/6m+1/2=2/3m+4

Solution for 5/6m+1/2=2/3m+4 equation:

5/6m+1/2=2/3m+4

We move all terms to the left:

5/6m+1/2-(2/3m+4)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 3m+4)!=0

m∈R


We get rid of parentheses

5/6m-2/3m-4+1/2=0

We calculate fractions


54m^2/72m^2+60m/72m^2+(-48m)/72m^2-4=0

We multiply all the terms by the denominator


54m^2+60m+(-48m)-4*72m^2=0

Wy multiply elements

54m^2-288m^2+60m+(-48m)=0

We get rid of parentheses

54m^2-288m^2+60m-48m=0

We add all the numbers together, and all the variables

-234m^2+12m=0

a = -234; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-234)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-234}=\frac{-24}{-468}
=2/39
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-234}=\frac{0}{-468}
=0
$