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

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

(X-3)(X-7)=3

We move all terms to the left:

(X-3)(X-7)-(3)=0

We multiply parentheses ..

(+X^2-7X-3X+21)-3=0

We get rid of parentheses

X^2-7X-3X+21-3=0

We add all the numbers together, and all the variables

X^2-10X+18=0

a = 1; b = -10; c = +18;
Δ = b2-4ac
Δ = -102-4·1·18
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*1}=\frac{10-2\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*1}=\frac{10+2\sqrt{7}}{2}
$