4/5a+3=1/3a-8

Solution for 4/5a+3=1/3a-8 equation:

4/5a+3=1/3a-8

We move all terms to the left:

4/5a+3-(1/3a-8)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 3a-8)!=0

a∈R


We get rid of parentheses

4/5a-1/3a+8+3=0

We calculate fractions


12a/15a^2+(-5a)/15a^2+8+3=0

We add all the numbers together, and all the variables

12a/15a^2+(-5a)/15a^2+11=0

We multiply all the terms by the denominator


12a+(-5a)+11*15a^2=0

Wy multiply elements

165a^2+12a+(-5a)=0

We get rid of parentheses

165a^2+12a-5a=0

We add all the numbers together, and all the variables

165a^2+7a=0

a = 165; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·165·0
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*165}=\frac{-14}{330}
=-7/165
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*165}=\frac{0}{330}
=0
$