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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x(x-1)

We multiply parentheses

x^2-1x

Back to the equation:

-(x^2-1x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-4x-5=0

a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
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{-(-4)-6}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2}
=5
$