2/3e-1/6e=-3

Solution for 2/3e-1/6e=-3 equation:

2/3e-1/6e=-3

We move all terms to the left:

2/3e-1/6e-(-3)=0


Domain of the equation: 3e!=0

e!=0/3

e!=0

e∈R



Domain of the equation: 6e!=0

e!=0/6

e!=0

e∈R


We add all the numbers together, and all the variables

2/3e-1/6e+3=0

We calculate fractions


12e/18e^2+(-3e)/18e^2+3=0

We multiply all the terms by the denominator


12e+(-3e)+3*18e^2=0

Wy multiply elements

54e^2+12e+(-3e)=0

We get rid of parentheses

54e^2+12e-3e=0

We add all the numbers together, and all the variables

54e^2+9e=0

a = 54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·54·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*54}=\frac{-18}{108}
=-1/6
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*54}=\frac{0}{108}
=0
$