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-256x^2-128x+175=0
a = -256; b = -128; c = +175;
Δ = b2-4ac
Δ = -1282-4·(-256)·175
Δ = 195584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{195584}=\sqrt{1024*191}=\sqrt{1024}*\sqrt{191}=32\sqrt{191}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-32\sqrt{191}}{2*-256}=\frac{128-32\sqrt{191}}{-512} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+32\sqrt{191}}{2*-256}=\frac{128+32\sqrt{191}}{-512} $
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