0.3n(n-5)=0.4-0.2n

Solution for 0.3n(n-5)=0.4-0.2n equation:

0.3n(n-5)=0.4-0.2n

We move all terms to the left:

0.3n(n-5)-(0.4-0.2n)=0

We add all the numbers together, and all the variables

0.3n(n-5)-(-0.2n+0.4)=0

We multiply parentheses

0n^2+0n-(-0.2n+0.4)=0

We get rid of parentheses

0n^2+0n+0.2n-0.4=0

We add all the numbers together, and all the variables

n^2+1.2n-0.4=0

a = 1; b = 1.2; c = -0.4;
Δ = b2-4ac
Δ = 1.22-4·1·(-0.4)
Δ = 3.04
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{-(1.2)-\sqrt{3.04}}{2*1}=\frac{-1.2-\sqrt{3.04}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.2)+\sqrt{3.04}}{2*1}=\frac{-1.2+\sqrt{3.04}}{2}
$