3x^2=6x(5x-9)

Solution for 3x^2=6x(5x-9) equation:

3x^2=6x(5x-9)

We move all terms to the left:

3x^2-(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

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

We add all the numbers together, and all the variables

-27x^2+54x=0

a = -27; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-27)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-27}=\frac{-108}{-54}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-27}=\frac{0}{-54}
=0
$