5n-4/n-1=4/2

Solution for 5n-4/n-1=4/2 equation:

5n-4/n-1=4/2

We move all terms to the left:

5n-4/n-1-(4/2)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

5n-4/n-1-2=0

We add all the numbers together, and all the variables

5n-4/n-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

5n^2-3n-4=0

a = 5; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·5·(-4)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*5}=\frac{3-\sqrt{89}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*5}=\frac{3+\sqrt{89}}{10}
$