F(3)=3x^2-10

Solution for F(3)=3x^2-10 equation:

(3)=3F^2-10

We move all terms to the left:

(3)-(3F^2-10)=0

We get rid of parentheses

-3F^2+10+3=0

We add all the numbers together, and all the variables

-3F^2+13=0

a = -3; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-3)·13
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{39}}{2*-3}=\frac{0-2\sqrt{39}}{-6}
=-\frac{2\sqrt{39}}{-6}
=-\frac{\sqrt{39}}{-3}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{39}}{2*-3}=\frac{0+2\sqrt{39}}{-6}
=\frac{2\sqrt{39}}{-6}
=\frac{\sqrt{39}}{-3}
$