a+2/3a=230

Solution for a+2/3a=230 equation:

a+2/3a=230

We move all terms to the left:

a+2/3a-(230)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply all the terms by the denominator


a*3a-230*3a+2=0

Wy multiply elements

3a^2-690a+2=0

a = 3; b = -690; c = +2;
Δ = b2-4ac
Δ = -6902-4·3·2
Δ = 476076
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:

$\sqrt{\Delta}=\sqrt{476076}=\sqrt{4*119019}=\sqrt{4}*\sqrt{119019}=2\sqrt{119019}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-690)-2\sqrt{119019}}{2*3}=\frac{690-2\sqrt{119019}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-690)+2\sqrt{119019}}{2*3}=\frac{690+2\sqrt{119019}}{6}
$