4/5e-4=2/3e

Solution for 4/5e-4=2/3e equation:

4/5e-4=2/3e

We move all terms to the left:

4/5e-4-(2/3e)=0


Domain of the equation: 5e!=0

e!=0/5

e!=0

e∈R



Domain of the equation: 3e)!=0

e!=0/1

e!=0

e∈R


We add all the numbers together, and all the variables

4/5e-(+2/3e)-4=0

We get rid of parentheses

4/5e-2/3e-4=0

We calculate fractions


12e/15e^2+(-10e)/15e^2-4=0

We multiply all the terms by the denominator


12e+(-10e)-4*15e^2=0

Wy multiply elements

-60e^2+12e+(-10e)=0

We get rid of parentheses

-60e^2+12e-10e=0

We add all the numbers together, and all the variables

-60e^2+2e=0

a = -60; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-60)·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*-60}=\frac{-4}{-120}
=1/30
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-60}=\frac{0}{-120}
=0
$