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

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

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

We move all terms to the left:

2x(x-3)-(6x^2-9x)=0

We multiply parentheses

2x^2-6x-(6x^2-9x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+3x=0

a = -4; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-4}=\frac{-6}{-8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-4}=\frac{0}{-8}
=0
$