0=24x^2-10x-1

Solution for 0=24x^2-10x-1 equation:

0=24x^2-10x-1

We move all terms to the left:

0-(24x^2-10x-1)=0

We add all the numbers together, and all the variables

-(24x^2-10x-1)=0

We get rid of parentheses

-24x^2+10x+1=0

a = -24; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-24)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-24}=\frac{-24}{-48}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-24}=\frac{4}{-48}
=-1/12
$