3x=x(7+3x)

Solution for 3x=x(7+3x) equation:

3x=x(7+3x)

We move all terms to the left:

3x-(x(7+3x))=0

We add all the numbers together, and all the variables

3x-(x(3x+7))=0


We calculate terms in parentheses: -(x(3x+7)), so:

x(3x+7)

We multiply parentheses

3x^2+7x

Back to the equation:

-(3x^2+7x)


We get rid of parentheses

-3x^2+3x-7x=0

We add all the numbers together, and all the variables

-3x^2-4x=0

a = -3; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-3)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-3}=\frac{8}{-6}
=-1+1/3
$