(x-1)(x+1)=10/14

Solution for (x-1)(x+1)=10/14 equation:

(x-1)(x+1)=10/14

We move all terms to the left:

(x-1)(x+1)-(10/14)=0

We add all the numbers together, and all the variables

(x-1)(x+1)-(+10/14)=0

We use the square of the difference formula

x^2-1-(+10/14)=0

We get rid of parentheses

x^2-1-10/14=0

We multiply all the terms by the denominator


x^2*14-10-1*14=0

We add all the numbers together, and all the variables

x^2*14-24=0

Wy multiply elements

14x^2-24=0

a = 14; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·14·(-24)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{21}}{2*14}=\frac{0-8\sqrt{21}}{28}
=-\frac{8\sqrt{21}}{28}
=-\frac{2\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{21}}{2*14}=\frac{0+8\sqrt{21}}{28}
=\frac{8\sqrt{21}}{28}
=\frac{2\sqrt{21}}{7}
$