4e(5e-1)+8=12

Solution for 4e(5e-1)+8=12 equation:

4e(5e-1)+8=12

We move all terms to the left:

4e(5e-1)+8-(12)=0

We add all the numbers together, and all the variables

4e(5e-1)-4=0

We multiply parentheses

20e^2-4e-4=0

a = 20; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·20·(-4)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{21}}{2*20}=\frac{4-4\sqrt{21}}{40}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{21}}{2*20}=\frac{4+4\sqrt{21}}{40}
$