3/7e+4=e

Solution for 3/7e+4=e equation:

3/7e+4=e

We move all terms to the left:

3/7e+4-(e)=0


Domain of the equation: 7e!=0

e!=0/7

e!=0

e∈R


We add all the numbers together, and all the variables

-1e+3/7e+4=0

We multiply all the terms by the denominator


-1e*7e+4*7e+3=0

Wy multiply elements

-7e^2+28e+3=0

a = -7; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·(-7)·3
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{217}}{2*-7}=\frac{-28-2\sqrt{217}}{-14}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{217}}{2*-7}=\frac{-28+2\sqrt{217}}{-14}
$