t=-4.9t^2+34.3t+12^3

Solution for t=-4.9t^2+34.3t+12^3 equation:

t=-4.9t^2+34.3t+12^3

We move all terms to the left:

t-(-4.9t^2+34.3t+12^3)=0

We get rid of parentheses

4.9t^2-34.3t+t-12^3=0

We add all the numbers together, and all the variables

4.9t^2-33.3t-1728=0

a = 4.9; b = -33.3; c = -1728;
Δ = b2-4ac
Δ = -33.32-4·4.9·(-1728)
Δ = 34977.69
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{-(-33.3)-\sqrt{34977.69}}{2*4.9}=\frac{33.3-\sqrt{34977.69}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33.3)+\sqrt{34977.69}}{2*4.9}=\frac{33.3+\sqrt{34977.69}}{9.8}
$