F(x)=4x+x2

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

(F)=4F+F2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-F^2-4F+F=0

We add all the numbers together, and all the variables

-1F^2-3F=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$