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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3e^2+8e+15e-10=0

We add all the numbers together, and all the variables

-3e^2+23e-10=0

a = -3; b = 23; c = -10;
Δ = b2-4ac
Δ = 232-4·(-3)·(-10)
Δ = 409
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{-(23)-\sqrt{409}}{2*-3}=\frac{-23-\sqrt{409}}{-6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{409}}{2*-3}=\frac{-23+\sqrt{409}}{-6}
$