1/5n+3=6-n

Solution for 1/5n+3=6-n equation:

1/5n+3=6-n

We move all terms to the left:

1/5n+3-(6-n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

1/5n-(-1n+6)+3=0

We get rid of parentheses

1/5n+1n-6+3=0

We multiply all the terms by the denominator


1n*5n-6*5n+3*5n+1=0

Wy multiply elements

5n^2-30n+15n+1=0

We add all the numbers together, and all the variables

5n^2-15n+1=0

a = 5; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·5·1
Δ = 205
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{-(-15)-\sqrt{205}}{2*5}=\frac{15-\sqrt{205}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{205}}{2*5}=\frac{15+\sqrt{205}}{10}
$