F(x)=2x2-12x+11

Solution for F(x)=2x2-12x+11 equation:

(F)=2F^2-12F+11

We move all terms to the left:

(F)-(2F^2-12F+11)=0

We get rid of parentheses

-2F^2+F+12F-11=0

We add all the numbers together, and all the variables

-2F^2+13F-11=0

a = -2; b = 13; c = -11;
Δ = b2-4ac
Δ = 132-4·(-2)·(-11)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-9}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+9}{2*-2}=\frac{-4}{-4}
=1
$