x(x-1)=5(x-1)

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

x(x-1)=5(x-1)

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(x-1)), so:

5(x-1)

We multiply parentheses

5x-5

Back to the equation:

-(5x-5)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-6x+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$