x=5x(x+2)

Solution for x=5x(x+2) equation:

x=5x(x+2)

We move all terms to the left:

x-(5x(x+2))=0


We calculate terms in parentheses: -(5x(x+2)), so:

5x(x+2)

We multiply parentheses

5x^2+10x

Back to the equation:

-(5x^2+10x)


We get rid of parentheses

-5x^2+x-10x=0

We add all the numbers together, and all the variables

-5x^2-9x=0

a = -5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-5)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-5}=\frac{18}{-10}
=-1+4/5
$