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

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

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

We move all terms to the left:

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


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

-5x(x-1)-x

We add all the numbers together, and all the variables

-1x-5x(x-1)

We multiply parentheses

-5x^2-1x+5x

We add all the numbers together, and all the variables

-5x^2+4x

Back to the equation:

-(-5x^2+4x)


We get rid of parentheses

5x^2-4x-6=0

a = 5; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·5·(-6)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*5}=\frac{4-2\sqrt{34}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*5}=\frac{4+2\sqrt{34}}{10}
$