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

Solution for 4F(x)=x^2-5x+2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+9F-2=0

a = -1; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-1)·(-2)
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{-(9)-\sqrt{73}}{2*-1}=\frac{-9-\sqrt{73}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*-1}=\frac{-9+\sqrt{73}}{-2}
$