5n=42/n=7

Solution for 5n=42/n=7 equation:

5n=42/n=7

We move all terms to the left:

5n-(42/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-(+42/n)=0

We get rid of parentheses

5n-42/n=0

We multiply all the terms by the denominator


5n*n-42=0

Wy multiply elements

5n^2-42=0

a = 5; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·5·(-42)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*5}=\frac{0-2\sqrt{210}}{10}
=-\frac{2\sqrt{210}}{10}
=-\frac{\sqrt{210}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*5}=\frac{0+2\sqrt{210}}{10}
=\frac{2\sqrt{210}}{10}
=\frac{\sqrt{210}}{5}
$