4n^2-2n-240=0

Solution for 4n^2-2n-240=0 equation:

4n^2-2n-240=0

a = 4; b = -2; c = -240;
Δ = b2-4ac
Δ = -22-4·4·(-240)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-62}{2*4}=\frac{-60}{8}
=-7+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+62}{2*4}=\frac{64}{8}
=8
$