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

Solution for 2(x+1)=x(x-6) equation:

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(x(x-6)), so:

x(x-6)

We multiply parentheses

x^2-6x

Back to the equation:

-(x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-1)·2
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{2}}{2*-1}=\frac{-8-6\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{2}}{2*-1}=\frac{-8+6\sqrt{2}}{-2}
$