3/4n-5=-5+n

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

3/4n-5=-5+n

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4n^2+20n-20n+3=0

We add all the numbers together, and all the variables

-4n^2+3=0

a = -4; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-4)·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-4}=\frac{0-4\sqrt{3}}{-8}
=-\frac{4\sqrt{3}}{-8}
=-\frac{\sqrt{3}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-4}=\frac{0+4\sqrt{3}}{-8}
=\frac{4\sqrt{3}}{-8}
=\frac{\sqrt{3}}{-2}
$