F(x)=3x^2-9x+4

Solution for F(x)=3x^2-9x+4 equation:

(F)=3F^2-9F+4

We move all terms to the left:

(F)-(3F^2-9F+4)=0

We get rid of parentheses

-3F^2+F+9F-4=0

We add all the numbers together, and all the variables

-3F^2+10F-4=0

a = -3; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-3)·(-4)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*-3}=\frac{-10-2\sqrt{13}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*-3}=\frac{-10+2\sqrt{13}}{-6}
$