5/6e-2/3e=24

Solution for 5/6e-2/3e=24 equation:

5/6e-2/3e=24

We move all terms to the left:

5/6e-2/3e-(24)=0


Domain of the equation: 6e!=0

e!=0/6

e!=0

e∈R



Domain of the equation: 3e!=0

e!=0/3

e!=0

e∈R


We calculate fractions


15e/18e^2+(-12e)/18e^2-24=0

We multiply all the terms by the denominator


15e+(-12e)-24*18e^2=0

Wy multiply elements

-432e^2+15e+(-12e)=0

We get rid of parentheses

-432e^2+15e-12e=0

We add all the numbers together, and all the variables

-432e^2+3e=0

a = -432; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-432)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-432}=\frac{-6}{-864}
=1/144
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-432}=\frac{0}{-864}
=0
$