F(x)=5-3x^2

Solution for F(x)=5-3x^2 equation:

(F)=5-3F^2

We move all terms to the left:

(F)-(5-3F^2)=0

We get rid of parentheses

3F^2+F-5=0

a = 3; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·3·(-5)
Δ = 61
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{61}}{2*3}=\frac{-1-\sqrt{61}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*3}=\frac{-1+\sqrt{61}}{6}
$