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

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

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

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


21m/12m^2+(-20m)/12m^2+4-2=0

We add all the numbers together, and all the variables

21m/12m^2+(-20m)/12m^2+2=0

We multiply all the terms by the denominator


21m+(-20m)+2*12m^2=0

Wy multiply elements

24m^2+21m+(-20m)=0

We get rid of parentheses

24m^2+21m-20m=0

We add all the numbers together, and all the variables

24m^2+m=0

a = 24; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·24·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*24}=\frac{-2}{48}
=-1/24
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*24}=\frac{0}{48}
=0
$