1/2e+3=4+e

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

1/2e+3=4+e

We move all terms to the left:

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


Domain of the equation: 2e!=0

e!=0/2

e!=0

e∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-e*2e-4*2e+3*2e+1=0

Wy multiply elements

-2e^2-8e+6e+1=0

We add all the numbers together, and all the variables

-2e^2-2e+1=0

a = -2; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-2)·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*-2}=\frac{2-2\sqrt{3}}{-4}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*-2}=\frac{2+2\sqrt{3}}{-4}
$