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-16t^2+120t+6=0
a = -16; b = 120; c = +6;
Δ = b2-4ac
Δ = 1202-4·(-16)·6
Δ = 14784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14784}=\sqrt{64*231}=\sqrt{64}*\sqrt{231}=8\sqrt{231}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{231}}{2*-16}=\frac{-120-8\sqrt{231}}{-32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{231}}{2*-16}=\frac{-120+8\sqrt{231}}{-32} $
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