((7+x)(7+x))+((7-x)(7-x))=130

Solution for ((7+x)(7+x))+((7-x)(7-x))=130 equation:

((7+x)(7+x))+((7-x)(7-x))=130

We move all terms to the left:

((7+x)(7+x))+((7-x)(7-x))-(130)=0

We add all the numbers together, and all the variables

((x+7)(x+7))+((-1x+7)(-1x+7))-130=0

We multiply parentheses ..

((+x^2+7x+7x+49))+((-1x+7)(-1x+7))-130=0


We calculate terms in parentheses: +((+x^2+7x+7x+49)), so:

(+x^2+7x+7x+49)

We get rid of parentheses

x^2+7x+7x+49

We add all the numbers together, and all the variables

x^2+14x+49

Back to the equation:

+(x^2+14x+49)



We calculate terms in parentheses: +((-1x+7)(-1x+7)), so:

(-1x+7)(-1x+7)

We multiply parentheses ..

(+x^2-7x-7x+49)

We get rid of parentheses

x^2-7x-7x+49

We add all the numbers together, and all the variables

x^2-14x+49

Back to the equation:

+(x^2-14x+49)


We get rid of parentheses

x^2+x^2+14x-14x+49+49-130=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
$