6n^2-n-100=0

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

6n^2-n-100=0

We add all the numbers together, and all the variables

6n^2-1n-100=0

a = 6; b = -1; c = -100;
Δ = b2-4ac
Δ = -12-4·6·(-100)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*6}=\frac{-48}{12}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*6}=\frac{50}{12}
=4+1/6
$