5n-3/4n=2

Solution for 5n-3/4n=2 equation:

5n-3/4n=2

We move all terms to the left:

5n-3/4n-(2)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We multiply all the terms by the denominator


5n*4n-2*4n-3=0

Wy multiply elements

20n^2-8n-3=0

a = 20; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·20·(-3)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{19}}{2*20}=\frac{8-4\sqrt{19}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{19}}{2*20}=\frac{8+4\sqrt{19}}{40}
$