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x^2-16x-1152=0
a = 1; b = -16; c = -1152;
Δ = b2-4ac
Δ = -162-4·1·(-1152)
Δ = 4864
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{19}}{2*1}=\frac{16-16\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{19}}{2*1}=\frac{16+16\sqrt{19}}{2} $
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