14+3n=8n(-3n+12)

Solution for 14+3n=8n(-3n+12) equation:

14+3n=8n(-3n+12)

We move all terms to the left:

14+3n-(8n(-3n+12))=0


We calculate terms in parentheses: -(8n(-3n+12)), so:

8n(-3n+12)

We multiply parentheses

-24n^2+96n

Back to the equation:

-(-24n^2+96n)


We get rid of parentheses

24n^2-96n+3n+14=0

We add all the numbers together, and all the variables

24n^2-93n+14=0

a = 24; b = -93; c = +14;
Δ = b2-4ac
Δ = -932-4·24·14
Δ = 7305
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{-(-93)-\sqrt{7305}}{2*24}=\frac{93-\sqrt{7305}}{48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+\sqrt{7305}}{2*24}=\frac{93+\sqrt{7305}}{48}
$