4/3a+5=1/2a

Solution for 4/3a+5=1/2a equation:

4/3a+5=1/2a

We move all terms to the left:

4/3a+5-(1/2a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

4/3a-(+1/2a)+5=0

We get rid of parentheses

4/3a-1/2a+5=0

We calculate fractions


8a/6a^2+(-3a)/6a^2+5=0

We multiply all the terms by the denominator


8a+(-3a)+5*6a^2=0

Wy multiply elements

30a^2+8a+(-3a)=0

We get rid of parentheses

30a^2+8a-3a=0

We add all the numbers together, and all the variables

30a^2+5a=0

a = 30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·30·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*30}=\frac{-10}{60}
=-1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*30}=\frac{0}{60}
=0
$