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-16x^2-112x+192=0
a = -16; b = -112; c = +192;
Δ = b2-4ac
Δ = -1122-4·(-16)·192
Δ = 24832
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24832}=\sqrt{256*97}=\sqrt{256}*\sqrt{97}=16\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{97}}{2*-16}=\frac{112-16\sqrt{97}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{97}}{2*-16}=\frac{112+16\sqrt{97}}{-32} $
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