0=24x^2-1x-3

Solution for 0=24x^2-1x-3 equation:

0=24x^2-1x-3

We move all terms to the left:

0-(24x^2-1x-3)=0

We add all the numbers together, and all the variables

-(24x^2-1x-3)=0

We get rid of parentheses

-24x^2+1x+3=0

We add all the numbers together, and all the variables

-24x^2+x+3=0

a = -24; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-24)·3
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-24}=\frac{-18}{-48}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-24}=\frac{16}{-48}
=-1/3
$