12n(3n+0.7)=4(3n+2.1)+24n

Solution for 12n(3n+0.7)=4(3n+2.1)+24n equation:

12n(3n+0.7)=4(3n+2.1)+24n

We move all terms to the left:

12n(3n+0.7)-(4(3n+2.1)+24n)=0

We multiply parentheses

36n^2+8.4n-(4(3n+2.1)+24n)=0


We calculate terms in parentheses: -(4(3n+2.1)+24n), so:

4(3n+2.1)+24n

We add all the numbers together, and all the variables

24n+4(3n+2.1)

We multiply parentheses

24n+12n+8.4

We add all the numbers together, and all the variables

36n+8.4

Back to the equation:

-(36n+8.4)


We get rid of parentheses

36n^2+8.4n-36n-8.4=0

We add all the numbers together, and all the variables

36n^2-27.6n-8.4=0

a = 36; b = -27.6; c = -8.4;
Δ = b2-4ac
Δ = -27.62-4·36·(-8.4)
Δ = 1971.36
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{-(-27.6)-\sqrt{1971.36}}{2*36}=\frac{27.6-\sqrt{1971.36}}{72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27.6)+\sqrt{1971.36}}{2*36}=\frac{27.6+\sqrt{1971.36}}{72}
$