5.84t-4.9t^2=-101

Solution for 5.84t-4.9t^2=-101 equation:

5.84t-4.9t^2=-101

We move all terms to the left:

5.84t-4.9t^2-(-101)=0

We add all the numbers together, and all the variables

-4.9t^2+5.84t+101=0

a = -4.9; b = 5.84; c = +101;
Δ = b2-4ac
Δ = 5.842-4·(-4.9)·101
Δ = 2013.7056
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{-(5.84)-\sqrt{2013.7056}}{2*-4.9}=\frac{-5.84-\sqrt{2013.7056}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.84)+\sqrt{2013.7056}}{2*-4.9}=\frac{-5.84+\sqrt{2013.7056}}{-9.8}
$