(2x-1)(5x+2)=(2x-1)(3x-7)

Solution for (2x-1)(5x+2)=(2x-1)(3x-7) equation:

(2x-1)(5x+2)=(2x-1)(3x-7)

We move all terms to the left:

(2x-1)(5x+2)-((2x-1)(3x-7))=0

We multiply parentheses ..

(+10x^2+4x-5x-2)-((2x-1)(3x-7))=0


We calculate terms in parentheses: -((2x-1)(3x-7)), so:

(2x-1)(3x-7)

We multiply parentheses ..

(+6x^2-14x-3x+7)

We get rid of parentheses

6x^2-14x-3x+7

We add all the numbers together, and all the variables

6x^2-17x+7

Back to the equation:

-(6x^2-17x+7)


We get rid of parentheses

10x^2-6x^2+4x-5x+17x-2-7=0

We add all the numbers together, and all the variables

4x^2+16x-9=0

a = 4; b = 16; c = -9;
Δ = b2-4ac
Δ = 162-4·4·(-9)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*4}=\frac{4}{8}
=1/2
$