F3=3x2-8x+7

Solution for F3=3x2-8x+7 equation:

3=3F^2-8F+7

We move all terms to the left:

3-(3F^2-8F+7)=0

We get rid of parentheses

-3F^2+8F-7+3=0

We add all the numbers together, and all the variables

-3F^2+8F-4=0

a = -3; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·(-3)·(-4)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*-3}=\frac{-12}{-6}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*-3}=\frac{-4}{-6}
=2/3
$