16=4-3n(n-13)

Solution for 16=4-3n(n-13) equation:

16=4-3n(n-13)

We move all terms to the left:

16-(4-3n(n-13))=0


We calculate terms in parentheses: -(4-3n(n-13)), so:

4-3n(n-13)

determiningTheFunctionDomain
-3n(n-13)+4

We multiply parentheses

-3n^2+39n+4

Back to the equation:

-(-3n^2+39n+4)


We get rid of parentheses

3n^2-39n-4+16=0

We add all the numbers together, and all the variables

3n^2-39n+12=0

a = 3; b = -39; c = +12;
Δ = b2-4ac
Δ = -392-4·3·12
Δ = 1377
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-9\sqrt{17}}{2*3}=\frac{39-9\sqrt{17}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+9\sqrt{17}}{2*3}=\frac{39+9\sqrt{17}}{6}
$