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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-5x+6x-10)-((3x-5)(2x-1))=0


We calculate terms in parentheses: -((3x-5)(2x-1)), so:

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

We multiply parentheses ..

(+6x^2-3x-10x+5)

We get rid of parentheses

6x^2-3x-10x+5

We add all the numbers together, and all the variables

6x^2-13x+5

Back to the equation:

-(6x^2-13x+5)


We get rid of parentheses

3x^2-6x^2-5x+6x+13x-10-5=0

We add all the numbers together, and all the variables

-3x^2+14x-15=0

a = -3; b = 14; c = -15;
Δ = b2-4ac
Δ = 142-4·(-3)·(-15)
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{-(14)-4}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*-3}=\frac{-10}{-6}
=1+2/3
$