1/2a+16=4-2/3a

Solution for 1/2a+16=4-2/3a equation:

1/2a+16=4-2/3a

We move all terms to the left:

1/2a+16-(4-2/3a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/2a-(-2/3a+4)+16=0

We get rid of parentheses

1/2a+2/3a-4+16=0

We calculate fractions


3a/6a^2+4a/6a^2-4+16=0

We add all the numbers together, and all the variables

3a/6a^2+4a/6a^2+12=0

We multiply all the terms by the denominator


3a+4a+12*6a^2=0

We add all the numbers together, and all the variables

7a+12*6a^2=0

Wy multiply elements

72a^2+7a=0

a = 72; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·72·0
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*72}=\frac{-14}{144}
=-7/72
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*72}=\frac{0}{144}
=0
$