F(x)=(2x2-3)2

Solution for F(x)=(2x2-3)2 equation:

(F)=(2F^2-3)2

We move all terms to the left:

(F)-((2F^2-3)2)=0


We calculate terms in parentheses: -((2F^2-3)2), so:

(2F^2-3)2

We multiply parentheses

4F^2-6

Back to the equation:

-(4F^2-6)


We get rid of parentheses

-4F^2+F+6=0

a = -4; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-4)·6
Δ = 97
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{97}}{2*-4}=\frac{-1-\sqrt{97}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-4}=\frac{-1+\sqrt{97}}{-8}
$