F(x)=1.5-1.5x^2

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

(F)=1.5-1.5F^2

We move all terms to the left:

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

We get rid of parentheses

1.5F^2+F-1.5=0

a = 1.5; b = 1; c = -1.5;
Δ = b2-4ac
Δ = 12-4·1.5·(-1.5)
Δ = 10
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{10}}{2*1.5}=\frac{-1-\sqrt{10}}{3}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{10}}{2*1.5}=\frac{-1+\sqrt{10}}{3}
$