2/5*n=6

Solution for 2/5*n=6 equation:

2/5*n=6

We move all terms to the left:

2/5*n-(6)=0


Domain of the equation: 5*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-6*5*n+2=0

Wy multiply elements

-30n*n+2=0

Wy multiply elements

-30n^2+2=0

a = -30; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-30)·2
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-30}=\frac{0-4\sqrt{15}}{-60}
=-\frac{4\sqrt{15}}{-60}
=-\frac{\sqrt{15}}{-15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-30}=\frac{0+4\sqrt{15}}{-60}
=\frac{4\sqrt{15}}{-60}
=\frac{\sqrt{15}}{-15}
$