F(x)=38-6x^2

Solution for F(x)=38-6x^2 equation:

(F)=38-6F^2

We move all terms to the left:

(F)-(38-6F^2)=0

We get rid of parentheses

6F^2+F-38=0

a = 6; b = 1; c = -38;
Δ = b2-4ac
Δ = 12-4·6·(-38)
Δ = 913
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{913}}{2*6}=\frac{-1-\sqrt{913}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{913}}{2*6}=\frac{-1+\sqrt{913}}{12}
$