-6x=-5(x-1)x

Solution for -6x=-5(x-1)x equation:

-6x=-5(x-1)x

We move all terms to the left:

-6x-(-5(x-1)x)=0


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

-5(x-1)x

We multiply parentheses

-5x^2+5x

Back to the equation:

-(-5x^2+5x)


We get rid of parentheses

5x^2-5x-6x=0

We add all the numbers together, and all the variables

5x^2-11x=0

a = 5; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·5·0
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{-(-11)-11}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*5}=\frac{22}{10}
=2+1/5
$