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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


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

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

We multiply parentheses ..

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

We get rid of parentheses

-5x^2+3x-5x+3

We add all the numbers together, and all the variables

-5x^2-2x+3

Back to the equation:

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


We get rid of parentheses

-7x^2+5x^2-7x+5x+2x+5-3=0

We add all the numbers together, and all the variables

-2x^2+2=0

a = -2; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-2)·2
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{-(0)-4}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-2}=\frac{4}{-4}
=-1
$