a+1/a-2=3a

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

a+1/a-2=3a

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

-2a+1/a-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-2a^2-2a+1=0

a = -2; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-2)·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*-2}=\frac{2-2\sqrt{3}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*-2}=\frac{2+2\sqrt{3}}{-4}
$