(8+3e)e=2

Solution for (8+3e)e=2 equation:

(8+3e)e=2

We move all terms to the left:

(8+3e)e-(2)=0

We add all the numbers together, and all the variables

(3e+8)e-2=0

We multiply parentheses

3e^2+8e-2=0

a = 3; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·3·(-2)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*3}=\frac{-8-2\sqrt{22}}{6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*3}=\frac{-8+2\sqrt{22}}{6}
$