3a-2/a=2

Solution for 3a-2/a=2 equation:

3a-2/a=2

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


3a*a-2*a-2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

3a^2-2a-2=0

a = 3; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·3·(-2)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*3}=\frac{2-2\sqrt{7}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*3}=\frac{2+2\sqrt{7}}{6}
$