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4=-16t^2+132t+5.5
We move all terms to the left:
4-(-16t^2+132t+5.5)=0
We get rid of parentheses
16t^2-132t-5.5+4=0
We add all the numbers together, and all the variables
16t^2-132t-1.5=0
a = 16; b = -132; c = -1.5;
Δ = b2-4ac
Δ = -1322-4·16·(-1.5)
Δ = 17520
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17520}=\sqrt{16*1095}=\sqrt{16}*\sqrt{1095}=4\sqrt{1095}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{1095}}{2*16}=\frac{132-4\sqrt{1095}}{32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{1095}}{2*16}=\frac{132+4\sqrt{1095}}{32} $
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