-4.9t^2+24.5t+8.9=t

Solution for -4.9t^2+24.5t+8.9=t equation:

-4.9t^2+24.5t+8.9=t

We move all terms to the left:

-4.9t^2+24.5t+8.9-(t)=0

We add all the numbers together, and all the variables

-4.9t^2+23.5t+8.9=0

a = -4.9; b = 23.5; c = +8.9;
Δ = b2-4ac
Δ = 23.52-4·(-4.9)·8.9
Δ = 726.69
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{-(23.5)-\sqrt{726.69}}{2*-4.9}=\frac{-23.5-\sqrt{726.69}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23.5)+\sqrt{726.69}}{2*-4.9}=\frac{-23.5+\sqrt{726.69}}{-9.8}
$