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

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

(8)=3F^2-5F

We move all terms to the left:

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

We get rid of parentheses

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

a = -3; b = 5; c = +8;
Δ = b2-4ac
Δ = 52-4·(-3)·8
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-3}=\frac{6}{-6}
=-1
$