5/e+1=2e

Solution for 5/e+1=2e equation:

5/e+1=2e

We move all terms to the left:

5/e+1-(2e)=0


Domain of the equation: e!=0

e∈R


We add all the numbers together, and all the variables

-2e+5/e+1=0

We multiply all the terms by the denominator


-2e*e+1*e+5=0

We add all the numbers together, and all the variables

e-2e*e+5=0

Wy multiply elements

-2e^2+e+5=0

a = -2; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-2)·5
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{41}}{2*-2}=\frac{-1-\sqrt{41}}{-4}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*-2}=\frac{-1+\sqrt{41}}{-4}
$