a+2/3a=8

Solution for a+2/3a=8 equation:

a+2/3a=8

We move all terms to the left:

a+2/3a-(8)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply all the terms by the denominator


a*3a-8*3a+2=0

Wy multiply elements

3a^2-24a+2=0

a = 3; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·3·2
Δ = 552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*3}=\frac{24-2\sqrt{138}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*3}=\frac{24+2\sqrt{138}}{6}
$