4+11e=2+5e(2+6e)

Solution for 4+11e=2+5e(2+6e) equation:

4+11e=2+5e(2+6e)

We move all terms to the left:

4+11e-(2+5e(2+6e))=0

We add all the numbers together, and all the variables

11e-(2+5e(6e+2))+4=0


We calculate terms in parentheses: -(2+5e(6e+2)), so:

2+5e(6e+2)

determiningTheFunctionDomain
5e(6e+2)+2

We multiply parentheses

30e^2+10e+2

Back to the equation:

-(30e^2+10e+2)


We get rid of parentheses

-30e^2+11e-10e-2+4=0

We add all the numbers together, and all the variables

-30e^2+e+2=0

a = -30; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-30)·2
Δ = 241
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{-(1)-\sqrt{241}}{2*-30}=\frac{-1-\sqrt{241}}{-60}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*-30}=\frac{-1+\sqrt{241}}{-60}
$