t=1.5+30t-4.9t^2

Solution for t=1.5+30t-4.9t^2 equation:

t=1.5+30t-4.9t^2

We move all terms to the left:

t-(1.5+30t-4.9t^2)=0

We get rid of parentheses

4.9t^2-30t+t-1.5=0

We add all the numbers together, and all the variables

4.9t^2-29t-1.5=0

a = 4.9; b = -29; c = -1.5;
Δ = b2-4ac
Δ = -292-4·4.9·(-1.5)
Δ = 870.4
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{-(-29)-\sqrt{870.4}}{2*4.9}=\frac{29-\sqrt{870.4}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{870.4}}{2*4.9}=\frac{29+\sqrt{870.4}}{9.8}
$