((x-6)(x+6))/8+((x-8)(x+8))/6=14

Solution for ((x-6)(x+6))/8+((x-8)(x+8))/6=14 equation:

((x-6)(x+6))/8+((x-8)(x+8))/6=14

We move all terms to the left:

((x-6)(x+6))/8+((x-8)(x+8))/6-(14)=0

We use the square of the difference formula

x^2+x^2-36-64-14=0

We add all the numbers together, and all the variables

2x^2-114=0

a = 2; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·2·(-114)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{57}}{2*2}=\frac{0-4\sqrt{57}}{4}
=-\frac{4\sqrt{57}}{4}
=-\sqrt{57}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{57}}{2*2}=\frac{0+4\sqrt{57}}{4}
=\frac{4\sqrt{57}}{4}
=\sqrt{57}
$