24x^2-6x-1=0-

Solution for 24x^2-6x-1=0- equation:

24x^2-6x-1=0-

We move all terms to the left:

24x^2-6x-1-(0-)=0

We add all the numbers together, and all the variables

24x^2-6x-1-0=0

We add all the numbers together, and all the variables

24x^2-6x-1=0

a = 24; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·24·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*24}=\frac{6-2\sqrt{33}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*24}=\frac{6+2\sqrt{33}}{48}
$