3a+1/2a=6

Solution for 3a+1/2a=6 equation:

3a+1/2a=6

We move all terms to the left:

3a+1/2a-(6)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


3a*2a-6*2a+1=0

Wy multiply elements

6a^2-12a+1=0

a = 6; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·6·1
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*6}=\frac{12-2\sqrt{30}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*6}=\frac{12+2\sqrt{30}}{12}
$