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

Solution for -x(5x-1)=x^2-1) equation:

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+x=0

a = -6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-6}=\frac{-2}{-12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-6}=\frac{0}{-12}
=0
$