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

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

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

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-27a^2)/75a^2+300a/75a^2+(-175a)/75a^2=0

We multiply all the terms by the denominator


(-27a^2)+300a+(-175a)=0

We get rid of parentheses

-27a^2+300a-175a=0

We add all the numbers together, and all the variables

-27a^2+125a=0

a = -27; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·(-27)·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*-27}=\frac{-250}{-54}
=4+17/27
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*-27}=\frac{0}{-54}
=0
$