24x2+12x-2=0

Solution for 24x2+12x-2=0 equation:

24x^2+12x-2=0

a = 24; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·24·(-2)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*24}=\frac{-12-4\sqrt{21}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*24}=\frac{-12+4\sqrt{21}}{48}
$