F(x)=-1.5x^2+5

Solution for F(x)=-1.5x^2+5 equation:

(F)=-1.5F^2+5

We move all terms to the left:

(F)-(-1.5F^2+5)=0

We get rid of parentheses

1.5F^2+F-5=0

a = 1.5; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·1.5·(-5)
Δ = 31
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{-(1)-\sqrt{31}}{2*1.5}=\frac{-1-\sqrt{31}}{3}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{31}}{2*1.5}=\frac{-1+\sqrt{31}}{3}
$