1/3n+30=n

Solution for 1/3n+30=n equation:

1/3n+30=n

We move all terms to the left:

1/3n+30-(n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/3n+30=0

We multiply all the terms by the denominator


-1n*3n+30*3n+1=0

Wy multiply elements

-3n^2+90n+1=0

a = -3; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-3)·1
Δ = 8112
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:

$\sqrt{\Delta}=\sqrt{8112}=\sqrt{2704*3}=\sqrt{2704}*\sqrt{3}=52\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-52\sqrt{3}}{2*-3}=\frac{-90-52\sqrt{3}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+52\sqrt{3}}{2*-3}=\frac{-90+52\sqrt{3}}{-6}
$