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

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

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

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 3m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-180m^2)/432m^2+324m/432m^2+(-288m)/432m^2=0

We multiply all the terms by the denominator


(-180m^2)+324m+(-288m)=0

We get rid of parentheses

-180m^2+324m-288m=0

We add all the numbers together, and all the variables

-180m^2+36m=0

a = -180; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-180)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-180}=\frac{-72}{-360}
=1/5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-180}=\frac{0}{-360}
=0
$