7x^2+x=x(x-1)

Solution for 7x^2+x=x(x-1) equation:

7x^2+x=x(x-1)

We move all terms to the left:

7x^2+x-(x(x-1))=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

7x^2-x^2+x+1x=0

We add all the numbers together, and all the variables

6x^2+2x=0

a = 6; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·6·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*6}=\frac{0}{12}
=0
$