F(0)=3x^2-7x+4

Solution for F(0)=3x^2-7x+4 equation:

(0)=3F^2-7F+4

We move all terms to the left:

(0)-(3F^2-7F+4)=0

We add all the numbers together, and all the variables

-(3F^2-7F+4)=0

We get rid of parentheses

-3F^2+7F-4=0

a = -3; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·(-3)·(-4)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-3}=\frac{-6}{-6}
=1
$