((x2-6)/2)-((x2+4)/4)=5

Solution for ((x2-6)/2)-((x2+4)/4)=5 equation:

((x2-6)/2)-((x2+4)/4)=5

We move all terms to the left:

((x2-6)/2)-((x2+4)/4)-(5)=0

We add all the numbers together, and all the variables

((+x^2-6)/2)-((+x^2+4)/4)-5=0

We calculate fractions


(-2x^2-8)/()+(4x^2-24)/()-5=0

We multiply all the terms by the denominator


(-2x^2-8)+(4x^2-24)-5*()=0

We add all the numbers together, and all the variables

(-2x^2-8)+(4x^2-24)=0

We get rid of parentheses

-2x^2+4x^2-8-24=0

We add all the numbers together, and all the variables

2x^2-32=0

a = 2; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·2·(-32)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*2}=\frac{16}{4}
=4
$