40/n-7=n-4

Solution for 40/n-7=n-4 equation:

40/n-7=n-4

We move all terms to the left:

40/n-7-(n-4)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

40/n-n+4-7=0

We multiply all the terms by the denominator


-n*n+4*n-7*n+40=0

We add all the numbers together, and all the variables

-3n-n*n+40=0

Wy multiply elements

-1n^2-3n+40=0

a = -1; b = -3; c = +40;
Δ = b2-4ac
Δ = -32-4·(-1)·40
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*-1}=\frac{-10}{-2}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*-1}=\frac{16}{-2}
=-8
$