x(x+11)=2(x^2-2x+1)

Solution for x(x+11)=2(x^2-2x+1) equation:

x(x+11)=2(x^2-2x+1)

We move all terms to the left:

x(x+11)-(2(x^2-2x+1))=0

We multiply parentheses

x^2+11x-(2(x^2-2x+1))=0


We calculate terms in parentheses: -(2(x^2-2x+1)), so:

2(x^2-2x+1)

We multiply parentheses

2x^2-4x+2

Back to the equation:

-(2x^2-4x+2)


We get rid of parentheses

x^2-2x^2+11x+4x-2=0

We add all the numbers together, and all the variables

-1x^2+15x-2=0

a = -1; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·(-1)·(-2)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{217}}{2*-1}=\frac{-15-\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{217}}{2*-1}=\frac{-15+\sqrt{217}}{-2}
$