X(x-1)=5x

Solution for X(x-1)=5x equation:

X(X-1)=5X

We move all terms to the left:

X(X-1)-(5X)=0

We add all the numbers together, and all the variables

-5X+X(X-1)=0

We multiply parentheses

X^2-5X-1X=0

We add all the numbers together, and all the variables

X^2-6X=0

a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2}
=6
$