e-6=1/3e

Solution for e-6=1/3e equation:

e-6=1/3e

We move all terms to the left:

e-6-(1/3e)=0


Domain of the equation: 3e)!=0

e!=0/1

e!=0

e∈R


We add all the numbers together, and all the variables

e-(+1/3e)-6=0

We get rid of parentheses

e-1/3e-6=0

We multiply all the terms by the denominator


e*3e-6*3e-1=0

Wy multiply elements

3e^2-18e-1=0

a = 3; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·3·(-1)
Δ = 336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{21}}{2*3}=\frac{18-4\sqrt{21}}{6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{21}}{2*3}=\frac{18+4\sqrt{21}}{6}
$