F(x)=3x^2-8x-3

Solution for F(x)=3x^2-8x-3 equation:

(F)=3F^2-8F-3

We move all terms to the left:

(F)-(3F^2-8F-3)=0

We get rid of parentheses

-3F^2+F+8F+3=0

We add all the numbers together, and all the variables

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

a = -3; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-3)·3
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{-(9)-3\sqrt{13}}{2*-3}=\frac{-9-3\sqrt{13}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{13}}{2*-3}=\frac{-9+3\sqrt{13}}{-6}
$