(7+x)(9-x)+(7-x)(9+x)=76

Solution for (7+x)(9-x)+(7-x)(9+x)=76 equation:

(7+x)(9-x)+(7-x)(9+x)=76

We move all terms to the left:

(7+x)(9-x)+(7-x)(9+x)-(76)=0

We add all the numbers together, and all the variables

(x+7)(-1x+9)+(-1x+7)(x+9)-76=0

We multiply parentheses ..

(-1x^2+9x-7x+63)+(-1x+7)(x+9)-76=0

We get rid of parentheses

-1x^2+9x-7x+(-1x+7)(x+9)+63-76=0

We multiply parentheses ..

-1x^2+(-1x^2-9x+7x+63)+9x-7x+63-76=0

We add all the numbers together, and all the variables

-1x^2+(-1x^2-9x+7x+63)+2x-13=0

We get rid of parentheses

-1x^2-1x^2-9x+7x+2x+63-13=0

We add all the numbers together, and all the variables

-2x^2+50=0

a = -2; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-2)·50
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-2}=\frac{20}{-4}
=-5
$