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-(a+16)+1=0

We get rid of parentheses

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

We multiply all the terms by the denominator


-a*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 = 2049
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{2049}}{2*-3}=\frac{45-\sqrt{2049}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*-3}=\frac{45+\sqrt{2049}}{-6}
$