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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2-6F+2=0

a = 3; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·3·2
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*3}=\frac{6-2\sqrt{3}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*3}=\frac{6+2\sqrt{3}}{6}
$