n=5n+6/6n+5

Solution for n=5n+6/6n+5 equation:

n=5n+6/6n+5

We move all terms to the left:

n-(5n+6/6n+5)=0


Domain of the equation: 6n+5)!=0

n∈R


We get rid of parentheses

n-5n-6/6n-5=0

We multiply all the terms by the denominator


n*6n-5n*6n-5*6n-6=0

Wy multiply elements

6n^2-30n^2-30n-6=0

We add all the numbers together, and all the variables

-24n^2-30n-6=0

a = -24; b = -30; c = -6;
Δ = b2-4ac
Δ = -302-4·(-24)·(-6)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18}{2*-24}=\frac{12}{-48}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18}{2*-24}=\frac{48}{-48}
=-1
$