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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-1x^2+3x+5x-15)-(x+3)(x-5)-5=0

We get rid of parentheses

-1x^2+3x+5x-(x+3)(x-5)-15-5=0

We multiply parentheses ..

-1x^2-(+x^2-5x+3x-15)+3x+5x-15-5=0

We add all the numbers together, and all the variables

-1x^2-(+x^2-5x+3x-15)+8x-20=0

We get rid of parentheses

-1x^2-x^2+5x-3x+8x+15-20=0

We add all the numbers together, and all the variables

-2x^2+10x-5=0

a = -2; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·(-2)·(-5)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*-2}=\frac{-10-2\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*-2}=\frac{-10+2\sqrt{15}}{-4}
$