72x^2-36x-6=0

Solution for 72x^2-36x-6=0 equation:

72x^2-36x-6=0

a = 72; b = -36; c = -6;
Δ = b2-4ac
Δ = -362-4·72·(-6)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{21}}{2*72}=\frac{36-12\sqrt{21}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{21}}{2*72}=\frac{36+12\sqrt{21}}{144}
$