F(2)=3x^2+3x-7

Solution for F(2)=3x^2+3x-7 equation:

(2)=3F^2+3F-7

We move all terms to the left:

(2)-(3F^2+3F-7)=0

We get rid of parentheses

-3F^2-3F+7+2=0

We add all the numbers together, and all the variables

-3F^2-3F+9=0

a = -3; b = -3; c = +9;
Δ = b2-4ac
Δ = -32-4·(-3)·9
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{13}}{2*-3}=\frac{3-3\sqrt{13}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{13}}{2*-3}=\frac{3+3\sqrt{13}}{-6}
$