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450=16t^2
We move all terms to the left:
450-(16t^2)=0
a = -16; b = 0; c = +450;
Δ = b2-4ac
Δ = 02-4·(-16)·450
Δ = 28800
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{2}}{2*-16}=\frac{0-120\sqrt{2}}{-32} =-\frac{120\sqrt{2}}{-32} =-\frac{15\sqrt{2}}{-4} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{2}}{2*-16}=\frac{0+120\sqrt{2}}{-32} =\frac{120\sqrt{2}}{-32} =\frac{15\sqrt{2}}{-4} $
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