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64x^2-9x-729=0
a = 64; b = -9; c = -729;
Δ = b2-4ac
Δ = -92-4·64·(-729)
Δ = 186705
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{186705}=\sqrt{81*2305}=\sqrt{81}*\sqrt{2305}=9\sqrt{2305}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{2305}}{2*64}=\frac{9-9\sqrt{2305}}{128} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{2305}}{2*64}=\frac{9+9\sqrt{2305}}{128} $
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