10/n+6=n+3

Solution for 10/n+6=n+3 equation:

10/n+6=n+3

We move all terms to the left:

10/n+6-(n+3)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

10/n-n-3+6=0

We multiply all the terms by the denominator


-n*n-3*n+6*n+10=0

We add all the numbers together, and all the variables

3n-n*n+10=0

Wy multiply elements

-1n^2+3n+10=0

a = -1; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-1)·10
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*-1}=\frac{-10}{-2}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*-1}=\frac{4}{-2}
=-2
$