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x^2-128x-960=0
a = 1; b = -128; c = -960;
Δ = b2-4ac
Δ = -1282-4·1·(-960)
Δ = 20224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20224}=\sqrt{256*79}=\sqrt{256}*\sqrt{79}=16\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-16\sqrt{79}}{2*1}=\frac{128-16\sqrt{79}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+16\sqrt{79}}{2*1}=\frac{128+16\sqrt{79}}{2} $
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