(3/4)n=520

Solution for (3/4)n=520 equation:

(3/4)n=520

We move all terms to the left:

(3/4)n-(520)=0


Domain of the equation: 4)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+3/4)n-520=0

We multiply parentheses

3n^2-520=0

a = 3; b = 0; c = -520;
Δ = b2-4ac
Δ = 02-4·3·(-520)
Δ = 6240
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:

$\sqrt{\Delta}=\sqrt{6240}=\sqrt{16*390}=\sqrt{16}*\sqrt{390}=4\sqrt{390}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{390}}{2*3}=\frac{0-4\sqrt{390}}{6}
=-\frac{4\sqrt{390}}{6}
=-\frac{2\sqrt{390}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{390}}{2*3}=\frac{0+4\sqrt{390}}{6}
=\frac{4\sqrt{390}}{6}
=\frac{2\sqrt{390}}{3}
$