F(3)=3x^2-15

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

(3)=3F^2-15

We move all terms to the left:

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

We get rid of parentheses

-3F^2+15+3=0

We add all the numbers together, and all the variables

-3F^2+18=0

a = -3; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-3)·18
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-3}=\frac{0-6\sqrt{6}}{-6}
=-\frac{6\sqrt{6}}{-6}
=-\frac{\sqrt{6}}{-1}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-3}=\frac{0+6\sqrt{6}}{-6}
=\frac{6\sqrt{6}}{-6}
=\frac{\sqrt{6}}{-1}
$