1n(X-2)+1n(2X-3)=2.1n

Solution for 1n(X-2)+1n(2X-3)=2.1n equation:

1n(n-2)+1n(2n-3)=2.1n

We move all terms to the left:

1n(n-2)+1n(2n-3)-(2.1n)=0

We add all the numbers together, and all the variables

1n(n-2)+1n(2n-3)-(+2.1n)=0

We multiply parentheses

n^2+2n^2-2n-3n-(+2.1n)=0

We get rid of parentheses

n^2+2n^2-2n-3n-2.1n=0

We add all the numbers together, and all the variables

3n^2-7.1n=0

a = 3; b = -7.1; c = 0;
Δ = b2-4ac
Δ = -7.12-4·3·0
Δ = 50.41
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{-(-7.1)-\sqrt{50.41}}{2*3}=\frac{7.1-\sqrt{50.41}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.1)+\sqrt{50.41}}{2*3}=\frac{7.1+\sqrt{50.41}}{6}
$