40/n=14-n

Solution for 40/n=14-n equation:

40/n=14-n

We move all terms to the left:

40/n-(14-n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

40/n-(-1n+14)=0

We get rid of parentheses

40/n+1n-14=0

We multiply all the terms by the denominator


1n*n-14*n+40=0

We add all the numbers together, and all the variables

-14n+1n*n+40=0

Wy multiply elements

n^2-14n+40=0

a = 1; b = -14; c = +40;
Δ = b2-4ac
Δ = -142-4·1·40
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*1}=\frac{8}{2}
=4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*1}=\frac{20}{2}
=10
$