(x-3)(x-1)=323

Solution for (x-3)(x-1)=323 equation:

(x-3)(x-1)=323

We move all terms to the left:

(x-3)(x-1)-(323)=0

We multiply parentheses ..

(+x^2-1x-3x+3)-323=0

We get rid of parentheses

x^2-1x-3x+3-323=0

We add all the numbers together, and all the variables

x^2-4x-320=0

a = 1; b = -4; c = -320;
Δ = b2-4ac
Δ = -42-4·1·(-320)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-36}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+36}{2*1}=\frac{40}{2}
=20
$