F(X-3)=3x^2-5x-8

Solution for F(X-3)=3x^2-5x-8 equation:

(F-3)=3F^2-5F-8

We move all terms to the left:

(F-3)-(3F^2-5F-8)=0

We get rid of parentheses

-3F^2+F+5F-3+8=0

We add all the numbers together, and all the variables

-3F^2+6F+5=0

a = -3; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-3)·5
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{6}}{2*-3}=\frac{-6-4\sqrt{6}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{6}}{2*-3}=\frac{-6+4\sqrt{6}}{-6}
$