54x^2-54x-8=0

Solution for 54x^2-54x-8=0 equation:

54x^2-54x-8=0

a = 54; b = -54; c = -8;
Δ = b2-4ac
Δ = -542-4·54·(-8)
Δ = 4644
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:

$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{129}}{2*54}=\frac{54-6\sqrt{129}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{129}}{2*54}=\frac{54+6\sqrt{129}}{108}
$