0.3(n-5)(n-7)=0.4-0.2

Solution for 0.3(n-5)(n-7)=0.4-0.2 equation:

0.3(n-5)(n-7)=0.4-0.2

We move all terms to the left:

0.3(n-5)(n-7)-(0.4-0.2)=0

We add all the numbers together, and all the variables

0.3(n-5)(n-7)-(0.2)=0

We add all the numbers together, and all the variables

0.3(n-5)(n-7)-0.2=0

We multiply parentheses ..

0.3(+n^2-7n-5n+35)-0.2=0

We multiply parentheses

0.3n^2-2.1n-1.5n+10.5-0.2=0

We add all the numbers together, and all the variables

0.3n^2-3.6n+10.3=0

a = 0.3; b = -3.6; c = +10.3;
Δ = b2-4ac
Δ = -3.62-4·0.3·10.3
Δ = 0.6
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{-(-3.6)-\sqrt{0.6}}{2*0.3}=\frac{3.6-\sqrt{0.6}}{0.6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.6)+\sqrt{0.6}}{2*0.3}=\frac{3.6+\sqrt{0.6}}{0.6}
$