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

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

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

We move all terms to the left:

-(5)/(6)e-(2)/(3)e-(-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^2-27e=0

a = 432; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·432·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*432}=\frac{0}{864}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*432}=\frac{54}{864}
=1/16
$