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 add all the numbers together, and all the variables

5/6e-2/3e+24=0

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
$