5x-1=x2-1

Solution for 5x-1=x2-1 equation:

5x-1=x2-1

We move all terms to the left:

5x-1-(x2-1)=0

We add all the numbers together, and all the variables

-(+x^2-1)+5x-1=0

We get rid of parentheses

-x^2+5x+1-1=0

We add all the numbers together, and all the variables

-1x^2+5x=0

a = -1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1}=\frac{0}{-2}
=0
$