X=30t-4.9t^2

Solution for X=30t-4.9t^2 equation:

X=30X-4.9X^2

We move all terms to the left:

X-(30X-4.9X^2)=0

We get rid of parentheses

4.9X^2-30X+X=0

We add all the numbers together, and all the variables

4.9X^2-29X=0

a = 4.9; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·4.9·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*4.9}=\frac{0}{9.8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*4.9}=\frac{58}{9.8}
=5+1/1.0888888888889
$