F(X)=6x^2-9x+3

Solution for F(X)=6x^2-9x+3 equation:

(F)=6F^2-9F+3

We move all terms to the left:

(F)-(6F^2-9F+3)=0

We get rid of parentheses

-6F^2+F+9F-3=0

We add all the numbers together, and all the variables

-6F^2+10F-3=0

a = -6; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-6)·(-3)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*-6}=\frac{-10-2\sqrt{7}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*-6}=\frac{-10+2\sqrt{7}}{-12}
$