F(6)=3x2+8x

Solution for F(6)=3x2+8x equation:

(6)=3F^2+8F

We move all terms to the left:

(6)-(3F^2+8F)=0

We get rid of parentheses

-3F^2-8F+6=0

a = -3; b = -8; c = +6;
Δ = b2-4ac
Δ = -82-4·(-3)·6
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*-3}=\frac{8-2\sqrt{34}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*-3}=\frac{8+2\sqrt{34}}{-6}
$