(5-3x)(4-7x)=(5-3x)(2+x)

Solution for (5-3x)(4-7x)=(5-3x)(2+x) equation:

(5-3x)(4-7x)=(5-3x)(2+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+21x^2-12x-35x+20)-((-3x+5)(x+2))=0


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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2-1x+10

Back to the equation:

-(-3x^2-1x+10)


We get rid of parentheses

21x^2+3x^2-12x-35x+1x+20-10=0

We add all the numbers together, and all the variables

24x^2-46x+10=0

a = 24; b = -46; c = +10;
Δ = b2-4ac
Δ = -462-4·24·10
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-34}{2*24}=\frac{12}{48}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+34}{2*24}=\frac{80}{48}
=1+2/3
$