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128x^2-56x-84=0
a = 128; b = -56; c = -84;
Δ = b2-4ac
Δ = -562-4·128·(-84)
Δ = 46144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{46144}=\sqrt{64*721}=\sqrt{64}*\sqrt{721}=8\sqrt{721}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{721}}{2*128}=\frac{56-8\sqrt{721}}{256} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{721}}{2*128}=\frac{56+8\sqrt{721}}{256} $
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