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0=-16t^2+48+64
We move all terms to the left:
0-(-16t^2+48+64)=0
We add all the numbers together, and all the variables
-(-16t^2+48+64)=0
We get rid of parentheses
16t^2-48-64=0
We add all the numbers together, and all the variables
16t^2-112=0
a = 16; b = 0; c = -112;
Δ = b2-4ac
Δ = 02-4·16·(-112)
Δ = 7168
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{7}}{2*16}=\frac{0-32\sqrt{7}}{32} =-\frac{32\sqrt{7}}{32} =-\sqrt{7} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{7}}{2*16}=\frac{0+32\sqrt{7}}{32} =\frac{32\sqrt{7}}{32} =\sqrt{7} $
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