2/3e-1=e-6

Solution for 2/3e-1=e-6 equation:

2/3e-1=e-6

We move all terms to the left:

2/3e-1-(e-6)=0


Domain of the equation: 3e!=0

e!=0/3

e!=0

e∈R


We get rid of parentheses

2/3e-e+6-1=0

We multiply all the terms by the denominator


-e*3e+6*3e-1*3e+2=0

Wy multiply elements

-3e^2+18e-3e+2=0

We add all the numbers together, and all the variables

-3e^2+15e+2=0

a = -3; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-3)·2
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{249}}{2*-3}=\frac{-15-\sqrt{249}}{-6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*-3}=\frac{-15+\sqrt{249}}{-6}
$