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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(4x(2x-1)), so:

4x(2x-1)

We multiply parentheses

8x^2-4x

Back to the equation:

-(8x^2-4x)


We get rid of parentheses

3x^2-8x^2+4x=0

We add all the numbers together, and all the variables

-5x^2+4x=0

a = -5; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-5)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-5}=\frac{-8}{-10}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-5}=\frac{0}{-10}
=0
$