54=4(n-1)2n

Solution for 54=4(n-1)2n equation:

54=4(n-1)2n

We move all terms to the left:

54-(4(n-1)2n)=0


We calculate terms in parentheses: -(4(n-1)2n), so:

4(n-1)2n

We multiply parentheses

8n^2-8n

Back to the equation:

-(8n^2-8n)


We get rid of parentheses

-8n^2+8n+54=0

a = -8; b = 8; c = +54;
Δ = b2-4ac
Δ = 82-4·(-8)·54
Δ = 1792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{7}}{2*-8}=\frac{-8-16\sqrt{7}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{7}}{2*-8}=\frac{-8+16\sqrt{7}}{-16}
$