F(x)=2X^2-4X+1F(-2)

Solution for F(x)=2X^2-4X+1F(-2) equation:

(F)=2F^2-4F+1(-2)

We move all terms to the left:

(F)-(2F^2-4F+1(-2))=0


We calculate terms in parentheses: -(2F^2-4F+1(-2)), so:

2F^2-4F+1(-2)

We add all the numbers together, and all the variables

2F^2-4F-2

Back to the equation:

-(2F^2-4F-2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+5F+2=0

a = -2; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-2)·2
Δ = 41
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{-(5)-\sqrt{41}}{2*-2}=\frac{-5-\sqrt{41}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*-2}=\frac{-5+\sqrt{41}}{-4}
$