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100=16t^2+48t+64
We move all terms to the left:
100-(16t^2+48t+64)=0
We get rid of parentheses
-16t^2-48t-64+100=0
We add all the numbers together, and all the variables
-16t^2-48t+36=0
a = -16; b = -48; c = +36;
Δ = b2-4ac
Δ = -482-4·(-16)·36
Δ = 4608
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48\sqrt{2}}{2*-16}=\frac{48-48\sqrt{2}}{-32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48\sqrt{2}}{2*-16}=\frac{48+48\sqrt{2}}{-32} $
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