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-4.9t^2+42t+3.5=75(t)
We move all terms to the left:
-4.9t^2+42t+3.5-(75(t))=0
determiningTheFunctionDomain -4.9t^2+42t-75t+3.5=0
We add all the numbers together, and all the variables
-4.9t^2-33t+3.5=0
a = -4.9; b = -33; c = +3.5;
Δ = b2-4ac
Δ = -332-4·(-4.9)·3.5
Δ = 1157.6
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{-(-33)-\sqrt{1157.6}}{2*-4.9}=\frac{33-\sqrt{1157.6}}{-9.8} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1157.6}}{2*-4.9}=\frac{33+\sqrt{1157.6}}{-9.8} $
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