F-3=-x(x+6)

Solution for F-3=-x(x+6) equation:

-3=-F(F+6)

We move all terms to the left:

-3-(-F(F+6))=0


We calculate terms in parentheses: -(-F(F+6)), so:

-F(F+6)

We multiply parentheses

-F^2-6F

We add all the numbers together, and all the variables

-1F^2-6F

Back to the equation:

-(-1F^2-6F)


We get rid of parentheses

1F^2+6F-3=0

We add all the numbers together, and all the variables

F^2+6F-3=0

a = 1; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·1·(-3)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*1}=\frac{-6-4\sqrt{3}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*1}=\frac{-6+4\sqrt{3}}{2}
$