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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(2(+x^2+5x-1x-5)), so:

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

We multiply parentheses

2x^2+10x-2x-10

We add all the numbers together, and all the variables

2x^2+8x-10

Back to the equation:

-(2x^2+8x-10)


We add all the numbers together, and all the variables

x^2-1x-(2x^2+8x-10)=0

We get rid of parentheses

x^2-2x^2-1x-8x+10=0

We add all the numbers together, and all the variables

-1x^2-9x+10=0

a = -1; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·(-1)·10
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*-1}=\frac{20}{-2}
=-10
$