F(x)=(3x^2-4)

Solution for F(x)=(3x^2-4) equation:

(F)=(3F^2-4)

We move all terms to the left:

(F)-((3F^2-4))=0


We calculate terms in parentheses: -((3F^2-4)), so:

(3F^2-4)

We get rid of parentheses

3F^2-4

Back to the equation:

-(3F^2-4)


We get rid of parentheses

-3F^2+F+4=0

a = -3; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-3)·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{-(1)-7}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-3}=\frac{6}{-6}
=-1
$