(x-5)*(x+5)-(x+5)*(x-5)=20

Solution for (x-5)*(x+5)-(x+5)*(x-5)=20 equation:

(x-5)(x+5)-(x+5)(x-5)=20

We move all terms to the left:

(x-5)(x+5)-(x+5)(x-5)-(20)=0

We use the square of the difference formula

x^2+x^2-25+25-20=0

We add all the numbers together, and all the variables

2x^2-20=0

a = 2; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·2·(-20)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*2}=\frac{0-4\sqrt{10}}{4}
=-\frac{4\sqrt{10}}{4}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*2}=\frac{0+4\sqrt{10}}{4}
=\frac{4\sqrt{10}}{4}
=\sqrt{10}
$