(n-10)(100/n)=40

Solution for (n-10)(100/n)=40 equation:

(n-10)(100/n)=40

We move all terms to the left:

(n-10)(100/n)-(40)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(n-10)(+100/n)-40=0

We multiply parentheses ..

(+100n^2-1000n)-40=0

We get rid of parentheses

100n^2-1000n-40=0

a = 100; b = -1000; c = -40;
Δ = b2-4ac
Δ = -10002-4·100·(-40)
Δ = 1016000
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:

$\sqrt{\Delta}=\sqrt{1016000}=\sqrt{1600*635}=\sqrt{1600}*\sqrt{635}=40\sqrt{635}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-40\sqrt{635}}{2*100}=\frac{1000-40\sqrt{635}}{200}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+40\sqrt{635}}{2*100}=\frac{1000+40\sqrt{635}}{200}
$