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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(6x(x+1)), so:

6x(x+1)

We multiply parentheses

6x^2+6x

Back to the equation:

-(6x^2+6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -6; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-6)·3
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{-(-3)-9}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-6}=\frac{12}{-12}
=-1
$