4(10n+4)n=2

Solution for 4(10n+4)n=2 equation:

4(10n+4)n=2

We move all terms to the left:

4(10n+4)n-(2)=0

We multiply parentheses

40n^2+16n-2=0

a = 40; b = 16; c = -2;
Δ = b2-4ac
Δ = 162-4·40·(-2)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*40}=\frac{-40}{80}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*40}=\frac{8}{80}
=1/10
$