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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-15x+7x-35)-((x-5)(5x-2))=0


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

(x-5)(5x-2)

We multiply parentheses ..

(+5x^2-2x-25x+10)

We get rid of parentheses

5x^2-2x-25x+10

We add all the numbers together, and all the variables

5x^2-27x+10

Back to the equation:

-(5x^2-27x+10)


We get rid of parentheses

3x^2-5x^2-15x+7x+27x-35-10=0

We add all the numbers together, and all the variables

-2x^2+19x-45=0

a = -2; b = 19; c = -45;
Δ = b2-4ac
Δ = 192-4·(-2)·(-45)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-1}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+1}{2*-2}=\frac{-18}{-4}
=4+1/2
$