(x-6)(x-5)=x

Solution for (x-6)(x-5)=x equation:

(x-6)(x-5)=x

We move all terms to the left:

(x-6)(x-5)-(x)=0

We add all the numbers together, and all the variables

-1x+(x-6)(x-5)=0

We multiply parentheses ..

(+x^2-5x-6x+30)-1x=0

We get rid of parentheses

x^2-5x-6x-1x+30=0

We add all the numbers together, and all the variables

x^2-12x+30=0

a = 1; b = -12; c = +30;
Δ = b2-4ac
Δ = -122-4·1·30
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{6}}{2*1}=\frac{12-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*1}=\frac{12+2\sqrt{6}}{2}
$