F(x)=3x^2-15

Solution for F(x)=3x^2-15 equation:

(F)=3F^2-15

We move all terms to the left:

(F)-(3F^2-15)=0

We get rid of parentheses

-3F^2+F+15=0

a = -3; b = 1; c = +15;
Δ = b2-4ac
Δ = 12-4·(-3)·15
Δ = 181
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{181}}{2*-3}=\frac{-1-\sqrt{181}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{181}}{2*-3}=\frac{-1+\sqrt{181}}{-6}
$