(5-x)(x-9)=(5-x)(7-x)

Solution for (5-x)(x-9)=(5-x)(7-x) equation:

(5-x)(x-9)=(5-x)(7-x)

We move all terms to the left:

(5-x)(x-9)-((5-x)(7-x))=0

We add all the numbers together, and all the variables

(-1x+5)(x-9)-((-1x+5)(-1x+7))=0

We multiply parentheses ..

(-1x^2+9x+5x-45)-((-1x+5)(-1x+7))=0


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

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

We multiply parentheses ..

(+x^2-7x-5x+35)

We get rid of parentheses

x^2-7x-5x+35

We add all the numbers together, and all the variables

x^2-12x+35

Back to the equation:

-(x^2-12x+35)


We get rid of parentheses

-1x^2-x^2+9x+5x+12x-45-35=0

We add all the numbers together, and all the variables

-2x^2+26x-80=0

a = -2; b = 26; c = -80;
Δ = b2-4ac
Δ = 262-4·(-2)·(-80)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6}{2*-2}=\frac{-20}{-4}
=+5
$