2/5n-2.5=n-1.2

Solution for 2/5n-2.5=n-1.2 equation:

2/5n-2.5=n-1.2

We move all terms to the left:

2/5n-2.5-(n-1.2)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

2/5n-n+1.2-2.5=0

We multiply all the terms by the denominator


-n*5n+(1.2)*5n-(2.5)*5n+2=0

We multiply parentheses

-n*5n+6n-12.5n+2=0

Wy multiply elements

-5n^2+6n-12.5n+2=0

We add all the numbers together, and all the variables

-5n^2-6.5n+2=0

a = -5; b = -6.5; c = +2;
Δ = b2-4ac
Δ = -6.52-4·(-5)·2
Δ = 82.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6.5)-\sqrt{82.25}}{2*-5}=\frac{6.5-\sqrt{82.25}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.5)+\sqrt{82.25}}{2*-5}=\frac{6.5+\sqrt{82.25}}{-10}
$