100=2n+6n^2

Solution for 100=2n+6n^2 equation:

100=2n+6n^2

We move all terms to the left:

100-(2n+6n^2)=0

We get rid of parentheses

-6n^2-2n+100=0

a = -6; b = -2; c = +100;
Δ = b2-4ac
Δ = -22-4·(-6)·100
Δ = 2404
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:

$\sqrt{\Delta}=\sqrt{2404}=\sqrt{4*601}=\sqrt{4}*\sqrt{601}=2\sqrt{601}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{601}}{2*-6}=\frac{2-2\sqrt{601}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{601}}{2*-6}=\frac{2+2\sqrt{601}}{-12}
$