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

Solution for F(x)=3x^2+6x-8 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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