2e-1/2e=5

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

2e-1/2e=5

We move all terms to the left:

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


Domain of the equation: 2e!=0

e!=0/2

e!=0

e∈R


We multiply all the terms by the denominator


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

Wy multiply elements

4e^2-10e-1=0

a = 4; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·4·(-1)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*4}=\frac{10-2\sqrt{29}}{8}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*4}=\frac{10+2\sqrt{29}}{8}
$