(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+4x-24=0

a = 1; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·1·(-24)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*1}=\frac{-4-4\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*1}=\frac{-4+4\sqrt{7}}{2}
$