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-4.9t^2+42t+3.5=75
We move all terms to the left:
-4.9t^2+42t+3.5-(75)=0
We add all the numbers together, and all the variables
-4.9t^2+42t-71.5=0
a = -4.9; b = 42; c = -71.5;
Δ = b2-4ac
Δ = 422-4·(-4.9)·(-71.5)
Δ = 362.6
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{-(42)-\sqrt{362.6}}{2*-4.9}=\frac{-42-\sqrt{362.6}}{-9.8} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+\sqrt{362.6}}{2*-4.9}=\frac{-42+\sqrt{362.6}}{-9.8} $
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