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0=-16t^2+55t+6.5
We move all terms to the left:
0-(-16t^2+55t+6.5)=0
We add all the numbers together, and all the variables
-(-16t^2+55t+6.5)=0
We get rid of parentheses
16t^2-55t-6.5=0
a = 16; b = -55; c = -6.5;
Δ = b2-4ac
Δ = -552-4·16·(-6.5)
Δ = 3441
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{3441}}{2*16}=\frac{55-\sqrt{3441}}{32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3441}}{2*16}=\frac{55+\sqrt{3441}}{32} $
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