3/8e-17-5/9e=11

Solution for 3/8e-17-5/9e=11 equation:

3/8e-17-5/9e=11

We move all terms to the left:

3/8e-17-5/9e-(11)=0


Domain of the equation: 8e!=0

e!=0/8

e!=0

e∈R



Domain of the equation: 9e!=0

e!=0/9

e!=0

e∈R


We add all the numbers together, and all the variables

3/8e-5/9e-28=0

We calculate fractions


27e/72e^2+(-40e)/72e^2-28=0

We multiply all the terms by the denominator


27e+(-40e)-28*72e^2=0

Wy multiply elements

-2016e^2+27e+(-40e)=0

We get rid of parentheses

-2016e^2+27e-40e=0

We add all the numbers together, and all the variables

-2016e^2-13e=0

a = -2016; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-2016)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-2016}=\frac{0}{-4032}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-2016}=\frac{26}{-4032}
=-13/2016
$