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0=-16t^2+124t+12
We move all terms to the left:
0-(-16t^2+124t+12)=0
We add all the numbers together, and all the variables
-(-16t^2+124t+12)=0
We get rid of parentheses
16t^2-124t-12=0
a = 16; b = -124; c = -12;
Δ = b2-4ac
Δ = -1242-4·16·(-12)
Δ = 16144
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16144}=\sqrt{16*1009}=\sqrt{16}*\sqrt{1009}=4\sqrt{1009}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-4\sqrt{1009}}{2*16}=\frac{124-4\sqrt{1009}}{32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+4\sqrt{1009}}{2*16}=\frac{124+4\sqrt{1009}}{32} $
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