5/9e-11/3e=3

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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 $

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