0=1.5t^2+2t-5

Solution for 0=1.5t^2+2t-5 equation:

0=1.5t^2+2t-5

We move all terms to the left:

0-(1.5t^2+2t-5)=0

We add all the numbers together, and all the variables

-(1.5t^2+2t-5)=0

We get rid of parentheses

-1.5t^2-2t+5=0

a = -1.5; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-1.5)·5
Δ = 34
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{-(-2)-\sqrt{34}}{2*-1.5}=\frac{2-\sqrt{34}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{34}}{2*-1.5}=\frac{2+\sqrt{34}}{-3}
$