5n-10=30/n=

Solution for 5n-10=30/n= equation:

5n-10=30/n=

We move all terms to the left:

5n-10-(30/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5n-(+30/n)-10=0

We get rid of parentheses

5n-30/n-10=0

We multiply all the terms by the denominator


5n*n-10*n-30=0

We add all the numbers together, and all the variables

-10n+5n*n-30=0

Wy multiply elements

5n^2-10n-30=0

a = 5; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·5·(-30)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{7}}{2*5}=\frac{10-10\sqrt{7}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{7}}{2*5}=\frac{10+10\sqrt{7}}{10}
$