e(5+7e)=21

Solution for e(5+7e)=21 equation:

e(5+7e)=21

We move all terms to the left:

e(5+7e)-(21)=0

We add all the numbers together, and all the variables

e(7e+5)-21=0

We multiply parentheses

7e^2+5e-21=0

a = 7; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·7·(-21)
Δ = 613
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{-(5)-\sqrt{613}}{2*7}=\frac{-5-\sqrt{613}}{14}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{613}}{2*7}=\frac{-5+\sqrt{613}}{14}
$