2a+1/6a=-4

Solution for 2a+1/6a=-4 equation:

2a+1/6a=-4

We move all terms to the left:

2a+1/6a-(-4)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We add all the numbers together, and all the variables

2a+1/6a+4=0

We multiply all the terms by the denominator


2a*6a+4*6a+1=0

Wy multiply elements

12a^2+24a+1=0

a = 12; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·12·1
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{33}}{2*12}=\frac{-24-4\sqrt{33}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{33}}{2*12}=\frac{-24+4\sqrt{33}}{24}
$