10=19.97t-4.9t^2

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Solution for 10=19.97t-4.9t^2 equation:



10=19.97t-4.9t^2
We move all terms to the left:
10-(19.97t-4.9t^2)=0
We get rid of parentheses
4.9t^2-19.97t+10=0
a = 4.9; b = -19.97; c = +10;
Δ = b2-4ac
Δ = -19.972-4·4.9·10
Δ = 202.8009
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{-(-19.97)-\sqrt{202.8009}}{2*4.9}=\frac{19.97-\sqrt{202.8009}}{9.8} $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.97)+\sqrt{202.8009}}{2*4.9}=\frac{19.97+\sqrt{202.8009}}{9.8} $

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