3x=6x(5x-9)

Solution for 3x=6x(5x-9) equation:

3x=6x(5x-9)

We move all terms to the left:

3x-(6x(5x-9))=0


We calculate terms in parentheses: -(6x(5x-9)), so:

6x(5x-9)

We multiply parentheses

30x^2-54x

Back to the equation:

-(30x^2-54x)


We get rid of parentheses

-30x^2+3x+54x=0

We add all the numbers together, and all the variables

-30x^2+57x=0

a = -30; b = 57; c = 0;
Δ = b2-4ac
Δ = 572-4·(-30)·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-57}{2*-30}=\frac{-114}{-60}
=1+9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+57}{2*-30}=\frac{0}{-60}
=0
$