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-16x^2+112x-124=0
a = -16; b = 112; c = -124;
Δ = b2-4ac
Δ = 1122-4·(-16)·(-124)
Δ = 4608
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-48\sqrt{2}}{2*-16}=\frac{-112-48\sqrt{2}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+48\sqrt{2}}{2*-16}=\frac{-112+48\sqrt{2}}{-32} $
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