12n(n+7)=4(21+3n)

Solution for 12n(n+7)=4(21+3n) equation:

12n(n+7)=4(21+3n)

We move all terms to the left:

12n(n+7)-(4(21+3n))=0

We add all the numbers together, and all the variables

12n(n+7)-(4(3n+21))=0

We multiply parentheses

12n^2+84n-(4(3n+21))=0


We calculate terms in parentheses: -(4(3n+21)), so:

4(3n+21)

We multiply parentheses

12n+84

Back to the equation:

-(12n+84)


We get rid of parentheses

12n^2+84n-12n-84=0

We add all the numbers together, and all the variables

12n^2+72n-84=0

a = 12; b = 72; c = -84;
Δ = b2-4ac
Δ = 722-4·12·(-84)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-96}{2*12}=\frac{-168}{24}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+96}{2*12}=\frac{24}{24}
=1
$