2x(x-1)=4x(2x-3)

Solution for 2x(x-1)=4x(2x-3) equation:

2x(x-1)=4x(2x-3)

We move all terms to the left:

2x(x-1)-(4x(2x-3))=0

We multiply parentheses

2x^2-2x-(4x(2x-3))=0


We calculate terms in parentheses: -(4x(2x-3)), so:

4x(2x-3)

We multiply parentheses

8x^2-12x

Back to the equation:

-(8x^2-12x)


We get rid of parentheses

2x^2-8x^2-2x+12x=0

We add all the numbers together, and all the variables

-6x^2+10x=0

a = -6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-6)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-6}=\frac{0}{-12}
=0
$