11=x(x-6)

Solution for 11=x(x-6) equation:

11=x(x-6)

We move all terms to the left:

11-(x(x-6))=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+6x+11=0

We add all the numbers together, and all the variables

-1x^2+6x+11=0

a = -1; b = 6; c = +11;
Δ = b2-4ac
Δ = 62-4·(-1)·11
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{5}}{2*-1}=\frac{-6-4\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{5}}{2*-1}=\frac{-6+4\sqrt{5}}{-2}
$