F(t)=-5t^2+10t+15

Solution for F(t)=-5t^2+10t+15 equation:

(F)=-5F^2+10F+15

We move all terms to the left:

(F)-(-5F^2+10F+15)=0

We get rid of parentheses

5F^2-10F+F-15=0

We add all the numbers together, and all the variables

5F^2-9F-15=0

a = 5; b = -9; c = -15;
Δ = b2-4ac
Δ = -92-4·5·(-15)
Δ = 381
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{381}}{2*5}=\frac{9-\sqrt{381}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{381}}{2*5}=\frac{9+\sqrt{381}}{10}
$