10=-5t^2+15t+0.5

Solution for 10=-5t^2+15t+0.5 equation:

10=-5t^2+15t+0.5

We move all terms to the left:

10-(-5t^2+15t+0.5)=0

We get rid of parentheses

5t^2-15t-0.5+10=0

We add all the numbers together, and all the variables

5t^2-15t+9.5=0

a = 5; b = -15; c = +9.5;
Δ = b2-4ac
Δ = -152-4·5·9.5
Δ = 35
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{35}}{2*5}=\frac{15-\sqrt{35}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{35}}{2*5}=\frac{15+\sqrt{35}}{10}
$