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

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}
$