4n^2-n-45=0

Solution for 4n^2-n-45=0 equation:

4n^2-n-45=0

We add all the numbers together, and all the variables

4n^2-1n-45=0

a = 4; b = -1; c = -45;
Δ = b2-4ac
Δ = -12-4·4·(-45)
Δ = 721
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{721}}{2*4}=\frac{1-\sqrt{721}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{721}}{2*4}=\frac{1+\sqrt{721}}{8}
$