6x(x+2)=3x(3x+1)

Solution for 6x(x+2)=3x(3x+1) equation:

6x(x+2)=3x(3x+1)

We move all terms to the left:

6x(x+2)-(3x(3x+1))=0

We multiply parentheses

6x^2+12x-(3x(3x+1))=0


We calculate terms in parentheses: -(3x(3x+1)), so:

3x(3x+1)

We multiply parentheses

9x^2+3x

Back to the equation:

-(9x^2+3x)


We get rid of parentheses

6x^2-9x^2+12x-3x=0

We add all the numbers together, and all the variables

-3x^2+9x=0

a = -3; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-3)·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*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-3}=\frac{0}{-6}
=0
$