F(x)^-1=2x^2-8x+3

Solution for F(x)^-1=2x^2-8x+3 equation:

(F)^-1=2F^2-8F+3

We move all terms to the left:

(F)^-1-(2F^2-8F+3)=0

We add all the numbers together, and all the variables

F-(2F^2-8F+3)-1=0

We get rid of parentheses

-2F^2+F+8F-3-1=0

We add all the numbers together, and all the variables

-2F^2+9F-4=0

a = -2; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·(-2)·(-4)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*-2}=\frac{-16}{-4}
=+4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*-2}=\frac{-2}{-4}
=1/2
$