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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

24a^2+a=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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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