F(x)=(6x^2-4)

Solution for F(x)=(6x^2-4) equation:

(F)=(6F^2-4)

We move all terms to the left:

(F)-((6F^2-4))=0


We calculate terms in parentheses: -((6F^2-4)), so:

(6F^2-4)

We get rid of parentheses

6F^2-4

Back to the equation:

-(6F^2-4)


We get rid of parentheses

-6F^2+F+4=0

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