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t=-16t^2+50t-24
We move all terms to the left:
t-(-16t^2+50t-24)=0
We get rid of parentheses
16t^2-50t+t+24=0
We add all the numbers together, and all the variables
16t^2-49t+24=0
a = 16; b = -49; c = +24;
Δ = b2-4ac
Δ = -492-4·16·24
Δ = 865
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{865}}{2*16}=\frac{49-\sqrt{865}}{32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{865}}{2*16}=\frac{49+\sqrt{865}}{32} $
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