3e=3e/4e+7+2

Solution for 3e=3e/4e+7+2 equation:

3e=3e/4e+7+2

We move all terms to the left:

3e-(3e/4e+7+2)=0


Domain of the equation: 4e+7+2)!=0

We move all terms containing e to the left, all other terms to the right

4e+2)!=-7

e∈R


We add all the numbers together, and all the variables

3e-(3e/4e+9)=0

We get rid of parentheses

3e-3e/4e-9=0

We multiply all the terms by the denominator


3e*4e-3e-9*4e=0

We add all the numbers together, and all the variables

-3e+3e*4e-9*4e=0

Wy multiply elements

12e^2-3e-36e=0

We add all the numbers together, and all the variables

12e^2-39e=0

a = 12; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·12·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*12}=\frac{0}{24}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*12}=\frac{78}{24}
=3+1/4
$