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64x^2-8x-128=0
a = 64; b = -8; c = -128;
Δ = b2-4ac
Δ = -82-4·64·(-128)
Δ = 32832
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32832}=\sqrt{576*57}=\sqrt{576}*\sqrt{57}=24\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24\sqrt{57}}{2*64}=\frac{8-24\sqrt{57}}{128} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24\sqrt{57}}{2*64}=\frac{8+24\sqrt{57}}{128} $
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