F(2)=3x^2-15

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

(2)=3F^2-15

We move all terms to the left:

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

We get rid of parentheses

-3F^2+15+2=0

We add all the numbers together, and all the variables

-3F^2+17=0

a = -3; b = 0; c = +17;
Δ = b2-4ac
Δ = 02-4·(-3)·17
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*-3}=\frac{0-2\sqrt{51}}{-6}
=-\frac{2\sqrt{51}}{-6}
=-\frac{\sqrt{51}}{-3}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*-3}=\frac{0+2\sqrt{51}}{-6}
=\frac{2\sqrt{51}}{-6}
=\frac{\sqrt{51}}{-3}
$