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4x^2-54x-729=0
a = 4; b = -54; c = -729;
Δ = b2-4ac
Δ = -542-4·4·(-729)
Δ = 14580
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14580}=\sqrt{2916*5}=\sqrt{2916}*\sqrt{5}=54\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54\sqrt{5}}{2*4}=\frac{54-54\sqrt{5}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54\sqrt{5}}{2*4}=\frac{54+54\sqrt{5}}{8} $
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