(X+1)(x-1)=2(x^2-13)

Solution for (X+1)(x-1)=2(x^2-13) equation:

(X+1)(X-1)=2(X^2-13)

We move all terms to the left:

(X+1)(X-1)-(2(X^2-13))=0

We use the square of the difference formula

X^2-(2(X^2-13))-1=0


We calculate terms in parentheses: -(2(X^2-13)), so:

2(X^2-13)

We multiply parentheses

2X^2-26

Back to the equation:

-(2X^2-26)


We get rid of parentheses

X^2-2X^2+26-1=0

We add all the numbers together, and all the variables

-1X^2+25=0

a = -1; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-1)·25
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-1}=\frac{-10}{-2}
=+5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-1}=\frac{10}{-2}
=-5
$