2n^2-14n-24=0

Solution for 2n^2-14n-24=0 equation:

2n^2-14n-24=0

a = 2; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·2·(-24)
Δ = 388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{97}}{2*2}=\frac{14-2\sqrt{97}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{97}}{2*2}=\frac{14+2\sqrt{97}}{4}
$