0=1.5(t^2)-6t+3

Solution for 0=1.5(t^2)-6t+3 equation:

0=1.5(t^2)-6t+3

We move all terms to the left:

0-(1.5(t^2)-6t+3)=0

We add all the numbers together, and all the variables

-(1.5t^2-6t+3)=0

We get rid of parentheses

-1.5t^2+6t-3=0

a = -1.5; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·(-1.5)·(-3)
Δ = 18
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-3\sqrt{2}}{2*-1.5}=\frac{-6-3\sqrt{2}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+3\sqrt{2}}{2*-1.5}=\frac{-6+3\sqrt{2}}{-3}
$