x=(4x+9)(x)

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

x=(4x+9)(x)

We move all terms to the left:

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


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

(4x+9)x

We multiply parentheses

4x^2+9x

Back to the equation:

-(4x^2+9x)


We get rid of parentheses

-4x^2+x-9x=0

We add all the numbers together, and all the variables

-4x^2-8x=0

a = -4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-4)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-4}=\frac{16}{-8}
=-2
$