2/3a+1=16-a

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

2/3a+1=16-a

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1a*3a-16*3a+1*3a+2=0

Wy multiply elements

3a^2-48a+3a+2=0

We add all the numbers together, and all the variables

3a^2-45a+2=0

a = 3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·3·2
Δ = 2001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2001}}{2*3}=\frac{45-\sqrt{2001}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2001}}{2*3}=\frac{45+\sqrt{2001}}{6}
$