F(x)=-4x(x+7)

Solution for F(x)=-4x(x+7) equation:

(F)=-4F(F+7)

We move all terms to the left:

(F)-(-4F(F+7))=0


We calculate terms in parentheses: -(-4F(F+7)), so:

-4F(F+7)

We multiply parentheses

-4F^2-28F

Back to the equation:

-(-4F^2-28F)


We get rid of parentheses

4F^2+28F+F=0

We add all the numbers together, and all the variables

4F^2+29F=0

a = 4; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·4·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*4}=\frac{-58}{8}
=-7+1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*4}=\frac{0}{8}
=0
$