2e(4e+3)-3e(e-5)=8

Solution for 2e(4e+3)-3e(e-5)=8 equation:

2e(4e+3)-3e(e-5)=8

We move all terms to the left:

2e(4e+3)-3e(e-5)-(8)=0

We multiply parentheses

8e^2-3e^2+6e+15e-8=0

We add all the numbers together, and all the variables

5e^2+21e-8=0

a = 5; b = 21; c = -8;
Δ = b2-4ac
Δ = 212-4·5·(-8)
Δ = 601
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{-(21)-\sqrt{601}}{2*5}=\frac{-21-\sqrt{601}}{10}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{601}}{2*5}=\frac{-21+\sqrt{601}}{10}
$