F(x)=1.5x2-2.5x-1.5

Solution for F(x)=1.5x2-2.5x-1.5 equation:

(F)=1.5F^2-2.5F-1.5

We move all terms to the left:

(F)-(1.5F^2-2.5F-1.5)=0

We get rid of parentheses

-1.5F^2+F+2.5F+1.5=0

We add all the numbers together, and all the variables

-1.5F^2+3.5F+1.5=0

a = -1.5; b = 3.5; c = +1.5;
Δ = b2-4ac
Δ = 3.52-4·(-1.5)·1.5
Δ = 21.25
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{21.25}}{2*-1.5}=\frac{-3.5-\sqrt{21.25}}{-3}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{21.25}}{2*-1.5}=\frac{-3.5+\sqrt{21.25}}{-3}
$