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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(6(x-1)3x), so:

6(x-1)3x

We multiply parentheses

18x^2-18x

Back to the equation:

-(18x^2-18x)


We get rid of parentheses

-18x^2+3x+18x+6=0

We add all the numbers together, and all the variables

-18x^2+21x+6=0

a = -18; b = 21; c = +6;
Δ = b2-4ac
Δ = 212-4·(-18)·6
Δ = 873
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{97}}{2*-18}=\frac{-21-3\sqrt{97}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{97}}{2*-18}=\frac{-21+3\sqrt{97}}{-36}
$