3/5*n=10

Solution for 3/5*n=10 equation:

3/5*n=10

We move all terms to the left:

3/5*n-(10)=0


Domain of the equation: 5*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-10*5*n+3=0

Wy multiply elements

-50n*n+3=0

Wy multiply elements

-50n^2+3=0

a = -50; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-50)·3
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-50}=\frac{0-10\sqrt{6}}{-100}
=-\frac{10\sqrt{6}}{-100}
=-\frac{\sqrt{6}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-50}=\frac{0+10\sqrt{6}}{-100}
=\frac{10\sqrt{6}}{-100}
=\frac{\sqrt{6}}{-10}
$