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

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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} $

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