8n^2-2n-45=0

Solution for 8n^2-2n-45=0 equation:

8n^2-2n-45=0

a = 8; b = -2; c = -45;
Δ = b2-4ac
Δ = -22-4·8·(-45)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*8}=\frac{-36}{16}
=-2+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*8}=\frac{40}{16}
=2+1/2
$