F(3)=4x^2-7x+6

Solution for F(3)=4x^2-7x+6 equation:

(3)=4F^2-7F+6

We move all terms to the left:

(3)-(4F^2-7F+6)=0

We get rid of parentheses

-4F^2+7F-6+3=0

We add all the numbers together, and all the variables

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

a = -4; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·(-4)·(-3)
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*-4}=\frac{-8}{-8}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-4}=\frac{-6}{-8}
=3/4
$