6a-1/2a=2

Solution for 6a-1/2a=2 equation:

6a-1/2a=2

We move all terms to the left:

6a-1/2a-(2)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


6a*2a-2*2a-1=0

Wy multiply elements

12a^2-4a-1=0

a = 12; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·12·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*12}=\frac{-4}{24}
=-1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*12}=\frac{12}{24}
=1/2
$