3/4m-1/2=2/3m+1

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

3/4m-1/2=2/3m+1

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 3m+1)!=0

m∈R


We get rid of parentheses

3/4m-2/3m-1-1/2=0

We calculate fractions


(-36m^2)/48m^2+36m/48m^2+(-32m)/48m^2-1=0

We multiply all the terms by the denominator


(-36m^2)+36m+(-32m)-1*48m^2=0

Wy multiply elements

(-36m^2)-48m^2+36m+(-32m)=0

We get rid of parentheses

-36m^2-48m^2+36m-32m=0

We add all the numbers together, and all the variables

-84m^2+4m=0

a = -84; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-84)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-84}=\frac{-8}{-168}
=1/21
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-84}=\frac{0}{-168}
=0
$