F(x)=6x^2-18x+12

Solution for F(x)=6x^2-18x+12 equation:

(F)=6F^2-18F+12

We move all terms to the left:

(F)-(6F^2-18F+12)=0

We get rid of parentheses

-6F^2+F+18F-12=0

We add all the numbers together, and all the variables

-6F^2+19F-12=0

a = -6; b = 19; c = -12;
Δ = b2-4ac
Δ = 192-4·(-6)·(-12)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{73}}{2*-6}=\frac{-19-\sqrt{73}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{73}}{2*-6}=\frac{-19+\sqrt{73}}{-12}
$