6x-x^2=-x

Solution for 6x-x^2=-x equation:

6x-x^2=-x

We move all terms to the left:

6x-x^2-(-x)=0

We add all the numbers together, and all the variables

-x^2+6x-(-1x)=0

We add all the numbers together, and all the variables

-1x^2+6x-(-1x)=0

We get rid of parentheses

-1x^2+6x+1x=0

We add all the numbers together, and all the variables

-1x^2+7x=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$