5/a-8/3a=46

Solution for 5/a-8/3a=46 equation:

5/a-8/3a=46

We move all terms to the left:

5/a-8/3a-(46)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We calculate fractions


15a/3a^2+(-8a)/3a^2-46=0

We multiply all the terms by the denominator


15a+(-8a)-46*3a^2=0

Wy multiply elements

-138a^2+15a+(-8a)=0

We get rid of parentheses

-138a^2+15a-8a=0

We add all the numbers together, and all the variables

-138a^2+7a=0

a = -138; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-138)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-138}=\frac{-14}{-276}
=7/138
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-138}=\frac{0}{-276}
=0
$