0=-1.5t^2+29t-100

Solution for 0=-1.5t^2+29t-100 equation:

0=-1.5t^2+29t-100

We move all terms to the left:

0-(-1.5t^2+29t-100)=0

We add all the numbers together, and all the variables

-(-1.5t^2+29t-100)=0

We get rid of parentheses

1.5t^2-29t+100=0

a = 1.5; b = -29; c = +100;
Δ = b2-4ac
Δ = -292-4·1.5·100
Δ = 241
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{241}}{2*1.5}=\frac{29-\sqrt{241}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{241}}{2*1.5}=\frac{29+\sqrt{241}}{3}
$