F(x)=15x^2-2

Solution for F(x)=15x^2-2 equation:

(F)=15F^2-2

We move all terms to the left:

(F)-(15F^2-2)=0

We get rid of parentheses

-15F^2+F+2=0

a = -15; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-15)·2
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*-15}=\frac{-12}{-30}
=2/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*-15}=\frac{10}{-30}
=-1/3
$