x=2x(3x+20)

Solution for x=2x(3x+20) equation:

x=2x(3x+20)

We move all terms to the left:

x-(2x(3x+20))=0


We calculate terms in parentheses: -(2x(3x+20)), so:

2x(3x+20)

We multiply parentheses

6x^2+40x

Back to the equation:

-(6x^2+40x)


We get rid of parentheses

-6x^2+x-40x=0

We add all the numbers together, and all the variables

-6x^2-39x=0

a = -6; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-6)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-6}=\frac{78}{-12}
=-6+1/2
$