36n^2-n-1=0

Solution for 36n^2-n-1=0 equation:

36n^2-n-1=0

We add all the numbers together, and all the variables

36n^2-1n-1=0

a = 36; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·36·(-1)
Δ = 145
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{145}}{2*36}=\frac{1-\sqrt{145}}{72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*36}=\frac{1+\sqrt{145}}{72}
$