0=t2-6t-1.5

Solution for 0=t2-6t-1.5 equation:

0=t2-6t-1.5

We move all terms to the left:

0-(t2-6t-1.5)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-t^2+6t+1.5=0

We add all the numbers together, and all the variables

-1t^2+6t+1.5=0

a = -1; b = 6; c = +1.5;
Δ = b2-4ac
Δ = 62-4·(-1)·1.5
Δ = 42
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{-(6)-\sqrt{42}}{2*-1}=\frac{-6-\sqrt{42}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{42}}{2*-1}=\frac{-6+\sqrt{42}}{-2}
$