5/9e-11/3e=3

Solution for 5/9e-11/3e=3 equation:

5/9e-11/3e=3

We move all terms to the left:

5/9e-11/3e-(3)=0


Domain of the equation: 9e!=0

e!=0/9

e!=0

e∈R



Domain of the equation: 3e!=0

e!=0/3

e!=0

e∈R


We calculate fractions


15e/27e^2+(-99e)/27e^2-3=0

We multiply all the terms by the denominator


15e+(-99e)-3*27e^2=0

Wy multiply elements

-81e^2+15e+(-99e)=0

We get rid of parentheses

-81e^2+15e-99e=0

We add all the numbers together, and all the variables

-81e^2-84e=0

a = -81; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·(-81)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*-81}=\frac{0}{-162}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*-81}=\frac{168}{-162}
=-1+1/27
$