24x^2-10x-4=0

Solution for 24x^2-10x-4=0 equation:

24x^2-10x-4=0

a = 24; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·24·(-4)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*24}=\frac{32}{48}
=2/3
$