1/2e-3=1/4e+2

Solution for 1/2e-3=1/4e+2 equation:

1/2e-3=1/4e+2

We move all terms to the left:

1/2e-3-(1/4e+2)=0


Domain of the equation: 2e!=0

e!=0/2

e!=0

e∈R



Domain of the equation: 4e+2)!=0

e∈R


We get rid of parentheses

1/2e-1/4e-2-3=0

We calculate fractions


4e/8e^2+(-2e)/8e^2-2-3=0

We add all the numbers together, and all the variables

4e/8e^2+(-2e)/8e^2-5=0

We multiply all the terms by the denominator


4e+(-2e)-5*8e^2=0

Wy multiply elements

-40e^2+4e+(-2e)=0

We get rid of parentheses

-40e^2+4e-2e=0

We add all the numbers together, and all the variables

-40e^2+2e=0

a = -40; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-40)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-40}=\frac{-4}{-80}
=1/20
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-40}=\frac{0}{-80}
=0
$