-114=35.2t+(0.5)(-9.8)t2

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Solution for -114=35.2t+(0.5)(-9.8)t2 equation:



-114=35.2t+(0.5)(-9.8)t2
We move all terms to the left:
-114-(35.2t+(0.5)(-9.8)t2)=0
We multiply parentheses ..
-(35.2t+(-4.9)t2)-114=0
We calculate terms in parentheses: -(35.2t+(-4.9)t2), so:
35.2t+(-4.9)t2
We multiply parentheses
-4.9t^2+35.2t
Back to the equation:
-(-4.9t^2+35.2t)
We get rid of parentheses
4.9t^2-35.2t-114=0
a = 4.9; b = -35.2; c = -114;
Δ = b2-4ac
Δ = -35.22-4·4.9·(-114)
Δ = 3473.44
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{-(-35.2)-\sqrt{3473.44}}{2*4.9}=\frac{35.2-\sqrt{3473.44}}{9.8} $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35.2)+\sqrt{3473.44}}{2*4.9}=\frac{35.2+\sqrt{3473.44}}{9.8} $

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