(x-7)(x-3)=x

Solution for (x-7)(x-3)=x equation:

(x-7)(x-3)=x

We move all terms to the left:

(x-7)(x-3)-(x)=0

We add all the numbers together, and all the variables

-1x+(x-7)(x-3)=0

We multiply parentheses ..

(+x^2-3x-7x+21)-1x=0

We get rid of parentheses

x^2-3x-7x-1x+21=0

We add all the numbers together, and all the variables

x^2-11x+21=0

a = 1; b = -11; c = +21;
Δ = b2-4ac
Δ = -112-4·1·21
Δ = 37
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{-(-11)-\sqrt{37}}{2*1}=\frac{11-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{37}}{2*1}=\frac{11+\sqrt{37}}{2}
$