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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((2x-1)(x+3)), so:

(2x-1)(x+3)

We multiply parentheses ..

(+2x^2+6x-1x-3)

We get rid of parentheses

2x^2+6x-1x-3

We add all the numbers together, and all the variables

2x^2+5x-3

Back to the equation:

-(2x^2+5x-3)


We get rid of parentheses

4x^2-2x^2-2x-2x-5x+1+3=0

We add all the numbers together, and all the variables

2x^2-9x+4=0

a = 2; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·2·4
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*2}=\frac{16}{4}
=4
$