n-3/5n=4

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

n-3/5n=4

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We multiply all the terms by the denominator


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

Wy multiply elements

5n^2-20n-3=0

a = 5; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·5·(-3)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{115}}{2*5}=\frac{20-2\sqrt{115}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{115}}{2*5}=\frac{20+2\sqrt{115}}{10}
$