x=2x(x+8)

Solution for x=2x(x+8) equation:

x=2x(x+8)

We move all terms to the left:

x-(2x(x+8))=0


We calculate terms in parentheses: -(2x(x+8)), so:

2x(x+8)

We multiply parentheses

2x^2+16x

Back to the equation:

-(2x^2+16x)


We get rid of parentheses

-2x^2+x-16x=0

We add all the numbers together, and all the variables

-2x^2-15x=0

a = -2; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-2)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-2}=\frac{30}{-4}
=-7+1/2
$