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

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

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

We move all terms to the left:

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


Domain of the equation: 2e!=0

e!=0/2

e!=0

e∈R



Domain of the equation: 3e-1)!=0

e∈R


We get rid of parentheses

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

We calculate fractions


3e/6e^2+(-4e)/6e^2+1+3=0

We add all the numbers together, and all the variables

3e/6e^2+(-4e)/6e^2+4=0

We multiply all the terms by the denominator


3e+(-4e)+4*6e^2=0

Wy multiply elements

24e^2+3e+(-4e)=0

We get rid of parentheses

24e^2+3e-4e=0

We add all the numbers together, and all the variables

24e^2-1e=0

a = 24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·24·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*24}=\frac{0}{48}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*24}=\frac{2}{48}
=1/24
$