16x^2-4x-24=0

Solution for 16x^2-4x-24=0 equation:

16x^2-4x-24=0

a = 16; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·16·(-24)
Δ = 1552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{97}}{2*16}=\frac{4-4\sqrt{97}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{97}}{2*16}=\frac{4+4\sqrt{97}}{32}
$