(2x-5)(5x+3)=(2x-5)(2x-1)

Solution for (2x-5)(5x+3)=(2x-5)(2x-1) equation:

(2x-5)(5x+3)=(2x-5)(2x-1)

We move all terms to the left:

(2x-5)(5x+3)-((2x-5)(2x-1))=0

We multiply parentheses ..

(+10x^2+6x-25x-15)-((2x-5)(2x-1))=0


We calculate terms in parentheses: -((2x-5)(2x-1)), so:

(2x-5)(2x-1)

We multiply parentheses ..

(+4x^2-2x-10x+5)

We get rid of parentheses

4x^2-2x-10x+5

We add all the numbers together, and all the variables

4x^2-12x+5

Back to the equation:

-(4x^2-12x+5)


We get rid of parentheses

10x^2-4x^2+6x-25x+12x-15-5=0

We add all the numbers together, and all the variables

6x^2-7x-20=0

a = 6; b = -7; c = -20;
Δ = b2-4ac
Δ = -72-4·6·(-20)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*6}=\frac{30}{12}
=2+1/2
$