144x^2-24x-1=0

Solution for 144x^2-24x-1=0 equation:

144x^2-24x-1=0

a = 144; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·144·(-1)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*144}=\frac{24-24\sqrt{2}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*144}=\frac{24+24\sqrt{2}}{288}
$