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-16x^2+128x+5=0
a = -16; b = 128; c = +5;
Δ = b2-4ac
Δ = 1282-4·(-16)·5
Δ = 16704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16704}=\sqrt{576*29}=\sqrt{576}*\sqrt{29}=24\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-24\sqrt{29}}{2*-16}=\frac{-128-24\sqrt{29}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+24\sqrt{29}}{2*-16}=\frac{-128+24\sqrt{29}}{-32} $
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