-5/6-e2/3e=24

Solution for -5/6-e2/3e=24 equation:

-5/6-e2/3e=24

We move all terms to the left:

-5/6-e2/3e-(24)=0


Domain of the equation: 3e!=0

e!=0/3

e!=0

e∈R


determiningTheFunctionDomain
-e2/3e-24-5/6=0

We calculate fractions


(-6e^2)/18e+(-15e)/18e-24=0

We multiply all the terms by the denominator


(-6e^2)+(-15e)-24*18e=0

Wy multiply elements

(-6e^2)+(-15e)-432e=0

We get rid of parentheses

-6e^2-15e-432e=0

We add all the numbers together, and all the variables

-6e^2-447e=0

a = -6; b = -447; c = 0;
Δ = b2-4ac
Δ = -4472-4·(-6)·0
Δ = 199809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{199809}=447$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-447)-447}{2*-6}=\frac{0}{-12}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-447)+447}{2*-6}=\frac{894}{-12}
=-74+1/2
$