F=x(4x+9)

Solution for F=x(4x+9) equation:

=F(4F+9)

We move all terms to the left:

-(F(4F+9))=0


We calculate terms in parentheses: -(F(4F+9)), so:

F(4F+9)

We multiply parentheses

4F^2+9F

Back to the equation:

-(4F^2+9F)


We get rid of parentheses

-4F^2-9F=0

a = -4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-4)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-4}=\frac{0}{-8}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-4}=\frac{18}{-8}
=-2+1/4
$