6n^2=n+16

Solution for 6n^2=n+16 equation:

6n^2=n+16

We move all terms to the left:

6n^2-(n+16)=0

We get rid of parentheses

6n^2-n-16=0

We add all the numbers together, and all the variables

6n^2-1n-16=0

a = 6; b = -1; c = -16;
Δ = b2-4ac
Δ = -12-4·6·(-16)
Δ = 385
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{-(-1)-\sqrt{385}}{2*6}=\frac{1-\sqrt{385}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{385}}{2*6}=\frac{1+\sqrt{385}}{12}
$