3+8e(5-e)=10

Solution for 3+8e(5-e)=10 equation:

3+8e(5-e)=10

We move all terms to the left:

3+8e(5-e)-(10)=0

We add all the numbers together, and all the variables

8e(-1e+5)+3-10=0

We add all the numbers together, and all the variables

8e(-1e+5)-7=0

We multiply parentheses

-8e^2+40e-7=0

a = -8; b = 40; c = -7;
Δ = b2-4ac
Δ = 402-4·(-8)·(-7)
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{86}}{2*-8}=\frac{-40-4\sqrt{86}}{-16}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{86}}{2*-8}=\frac{-40+4\sqrt{86}}{-16}
$