F(x)=x2-5x+4

Solution for F(x)=x2-5x+4 equation:

(F)=F2-5F+4

We move all terms to the left:

(F)-(F2-5F+4)=0

We add all the numbers together, and all the variables

-(+F^2-5F+4)+F=0

We get rid of parentheses

-F^2+5F+F-4=0

We add all the numbers together, and all the variables

-1F^2+6F-4=0

a = -1; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·(-1)·(-4)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*-1}=\frac{-6-2\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*-1}=\frac{-6+2\sqrt{5}}{-2}
$