F(x)=x2+6x

Solution for F(x)=x2+6x equation:

(F)=F2+6F

We move all terms to the left:

(F)-(F2+6F)=0

We add all the numbers together, and all the variables

-(+F^2+6F)+F=0

We get rid of parentheses

-F^2-6F+F=0

We add all the numbers together, and all the variables

-1F^2-5F=0

a = -1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-1}=\frac{0}{-2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-1}=\frac{10}{-2}
=-5
$