1.5=-5t^2+15t+8

Solution for 1.5=-5t^2+15t+8 equation:

1.5=-5t^2+15t+8

We move all terms to the left:

1.5-(-5t^2+15t+8)=0

We get rid of parentheses

5t^2-15t-8+1.5=0

We add all the numbers together, and all the variables

5t^2-15t-6.5=0

a = 5; b = -15; c = -6.5;
Δ = b2-4ac
Δ = -152-4·5·(-6.5)
Δ = 355
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{-(-15)-\sqrt{355}}{2*5}=\frac{15-\sqrt{355}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{355}}{2*5}=\frac{15+\sqrt{355}}{10}
$