24x2-36x-12=0

Solution for 24x2-36x-12=0 equation:

24x^2-36x-12=0

a = 24; b = -36; c = -12;
Δ = b2-4ac
Δ = -362-4·24·(-12)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{17}}{2*24}=\frac{36-12\sqrt{17}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{17}}{2*24}=\frac{36+12\sqrt{17}}{48}
$