F(x)=x2-5x2+4

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

(F)=F2-5F^2+4

We move all terms to the left:

(F)-(F2-5F^2+4)=0

We get rid of parentheses

5F^2-F2+F-4=0

We add all the numbers together, and all the variables

4F^2+F-4=0

a = 4; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·4·(-4)
Δ = 65
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{-(1)-\sqrt{65}}{2*4}=\frac{-1-\sqrt{65}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*4}=\frac{-1+\sqrt{65}}{8}
$