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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+5x^2-15x-7x+21)-((5x-7)(2x-1))=0


We calculate terms in parentheses: -((5x-7)(2x-1)), so:

(5x-7)(2x-1)

We multiply parentheses ..

(+10x^2-5x-14x+7)

We get rid of parentheses

10x^2-5x-14x+7

We add all the numbers together, and all the variables

10x^2-19x+7

Back to the equation:

-(10x^2-19x+7)


We get rid of parentheses

5x^2-10x^2-15x-7x+19x+21-7=0

We add all the numbers together, and all the variables

-5x^2-3x+14=0

a = -5; b = -3; c = +14;
Δ = b2-4ac
Δ = -32-4·(-5)·14
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*-5}=\frac{20}{-10}
=-2
$