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64x^2+120x-288=0
a = 64; b = 120; c = -288;
Δ = b2-4ac
Δ = 1202-4·64·(-288)
Δ = 88128
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{88128}=\sqrt{5184*17}=\sqrt{5184}*\sqrt{17}=72\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-72\sqrt{17}}{2*64}=\frac{-120-72\sqrt{17}}{128} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+72\sqrt{17}}{2*64}=\frac{-120+72\sqrt{17}}{128} $
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