10/3a+5=3/a+1

Solution for 10/3a+5=3/a+1 equation:

10/3a+5=3/a+1

We move all terms to the left:

10/3a+5-(3/a+1)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: a+1)!=0

a∈R


We get rid of parentheses

10/3a-3/a-1+5=0

We calculate fractions


10a/3a^2+(-9a)/3a^2-1+5=0

We add all the numbers together, and all the variables

10a/3a^2+(-9a)/3a^2+4=0

We multiply all the terms by the denominator


10a+(-9a)+4*3a^2=0

Wy multiply elements

12a^2+10a+(-9a)=0

We get rid of parentheses

12a^2+10a-9a=0

We add all the numbers together, and all the variables

12a^2+a=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
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*12}=\frac{-2}{24}
=-1/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$