(x-21)(x-7)=3

Solution for (x-21)(x-7)=3 equation:

(x-21)(x-7)=3

We move all terms to the left:

(x-21)(x-7)-(3)=0

We multiply parentheses ..

(+x^2-7x-21x+147)-3=0

We get rid of parentheses

x^2-7x-21x+147-3=0

We add all the numbers together, and all the variables

x^2-28x+144=0

a = 1; b = -28; c = +144;
Δ = b2-4ac
Δ = -282-4·1·144
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{13}}{2*1}=\frac{28-4\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{13}}{2*1}=\frac{28+4\sqrt{13}}{2}
$