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10=-4.9t^2+19.6t+58.8
We move all terms to the left:
10-(-4.9t^2+19.6t+58.8)=0
We get rid of parentheses
4.9t^2-19.6t-58.8+10=0
We add all the numbers together, and all the variables
4.9t^2-19.6t-48.8=0
a = 4.9; b = -19.6; c = -48.8;
Δ = b2-4ac
Δ = -19.62-4·4.9·(-48.8)
Δ = 1340.64
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{-(-19.6)-\sqrt{1340.64}}{2*4.9}=\frac{19.6-\sqrt{1340.64}}{9.8} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.6)+\sqrt{1340.64}}{2*4.9}=\frac{19.6+\sqrt{1340.64}}{9.8} $
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