2/5*n=10

Solution for 2/5*n=10 equation:

2/5*n=10

We move all terms to the left:

2/5*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+2=0

Wy multiply elements

-50n*n+2=0

Wy multiply elements

-50n^2+2=0

a = -50; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-50)·2
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-50}=\frac{-20}{-100}
=1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-50}=\frac{20}{-100}
=-1/5
$