144x^2+72x-6=0

Solution for 144x^2+72x-6=0 equation:

144x^2+72x-6=0

a = 144; b = 72; c = -6;
Δ = b2-4ac
Δ = 722-4·144·(-6)
Δ = 8640
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:

$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{15}}{2*144}=\frac{-72-24\sqrt{15}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{15}}{2*144}=\frac{-72+24\sqrt{15}}{288}
$