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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2-3x-(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

6x^2-8x^2-3x+4x=0

We add all the numbers together, and all the variables

-2x^2+x=0

a = -2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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