n/n-3+n=7n-18/n-3

Solution for n/n-3+n=7n-18/n-3 equation:

n/n-3+n=7n-18/n-3

We move all terms to the left:

n/n-3+n-(7n-18/n-3)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: n-3)!=0

n∈R


We add all the numbers together, and all the variables

n+n/n-(7n-18/n-3)-3=0

We get rid of parentheses

n+n/n-7n+18/n+3-3=0

Fractions to decimals

18/n+n-7n+3-3+1=0

We multiply all the terms by the denominator


n*n-7n*n+3*n-3*n+1*n+18=0

We add all the numbers together, and all the variables

n+n*n-7n*n+18=0

Wy multiply elements

n^2-7n^2+n+18=0

We add all the numbers together, and all the variables

-6n^2+n+18=0

a = -6; b = 1; c = +18;
Δ = b2-4ac
Δ = 12-4·(-6)·18
Δ = 433
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{-(1)-\sqrt{433}}{2*-6}=\frac{-1-\sqrt{433}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{433}}{2*-6}=\frac{-1+\sqrt{433}}{-12}
$