F(x)=-0.5^3+2.5x^2+4.5x-22.5

Solution for F(x)=-0.5^3+2.5x^2+4.5x-22.5 equation:

(F)=-0.5^3+2.5F^2+4.5F-22.5

We move all terms to the left:

(F)-(-0.5^3+2.5F^2+4.5F-22.5)=0

We get rid of parentheses

-2.5F^2-4.5F+F+22.5+0.5^3=0

We add all the numbers together, and all the variables

-2.5F^2-3.5F+22.625=0

a = -2.5; b = -3.5; c = +22.625;
Δ = b2-4ac
Δ = -3.52-4·(-2.5)·22.625
Δ = 238.5
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{-(-3.5)-\sqrt{238.5}}{2*-2.5}=\frac{3.5-\sqrt{238.5}}{-5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.5)+\sqrt{238.5}}{2*-2.5}=\frac{3.5+\sqrt{238.5}}{-5}
$