F(x)=6-5x^2

Solution for F(x)=6-5x^2 equation:

(F)=6-5F^2

We move all terms to the left:

(F)-(6-5F^2)=0

We get rid of parentheses

5F^2+F-6=0

a = 5; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·5·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*5}=\frac{-12}{10}
=-1+1/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*5}=\frac{10}{10}
=1
$