n=7/4n+5

Solution for n=7/4n+5 equation:

n=7/4n+5

We move all terms to the left:

n-(7/4n+5)=0


Domain of the equation: 4n+5)!=0

n∈R


We get rid of parentheses

n-7/4n-5=0

We multiply all the terms by the denominator


n*4n-5*4n-7=0

Wy multiply elements

4n^2-20n-7=0

a = 4; b = -20; c = -7;
Δ = b2-4ac
Δ = -202-4·4·(-7)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16\sqrt{2}}{2*4}=\frac{20-16\sqrt{2}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16\sqrt{2}}{2*4}=\frac{20+16\sqrt{2}}{8}
$