3(2n-14)n=14

Solution for 3(2n-14)n=14 equation:

3(2n-14)n=14

We move all terms to the left:

3(2n-14)n-(14)=0

We multiply parentheses

6n^2-42n-14=0

a = 6; b = -42; c = -14;
Δ = b2-4ac
Δ = -422-4·6·(-14)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-10\sqrt{21}}{2*6}=\frac{42-10\sqrt{21}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+10\sqrt{21}}{2*6}=\frac{42+10\sqrt{21}}{12}
$