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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·(-2)·(-3)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*-2}=\frac{-12}{-4}
=+3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*-2}=\frac{-2}{-4}
=1/2
$