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

Solution for (x-11)-x(x-6)=0 equation:

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

We multiply parentheses

-x^2+(x-11)+6x=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+7x-11=0

a = -1; b = 7; c = -11;
Δ = b2-4ac
Δ = 72-4·(-1)·(-11)
Δ = 5
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{-(7)-\sqrt{5}}{2*-1}=\frac{-7-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{5}}{2*-1}=\frac{-7+\sqrt{5}}{-2}
$