24x^2-12x-14=0

Solution for 24x^2-12x-14=0 equation:

24x^2-12x-14=0

a = 24; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·24·(-14)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{93}}{2*24}=\frac{12-4\sqrt{93}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{93}}{2*24}=\frac{12+4\sqrt{93}}{48}
$