6n^2-n-1275=0

Solution for 6n^2-n-1275=0 equation:

6n^2-n-1275=0

We add all the numbers together, and all the variables

6n^2-1n-1275=0

a = 6; b = -1; c = -1275;
Δ = b2-4ac
Δ = -12-4·6·(-1275)
Δ = 30601
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{30601}}{2*6}=\frac{1-\sqrt{30601}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{30601}}{2*6}=\frac{1+\sqrt{30601}}{12}
$