6*n^2-4n-100=0

Solution for 6*n^2-4n-100=0 equation:

6n^2-4n-100=0

a = 6; b = -4; c = -100;
Δ = b2-4ac
Δ = -42-4·6·(-100)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{151}}{2*6}=\frac{4-4\sqrt{151}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{151}}{2*6}=\frac{4+4\sqrt{151}}{12}
$