(x-2)(x-3)=42

Solution for (x-2)(x-3)=42 equation:

(x-2)(x-3)=42

We move all terms to the left:

(x-2)(x-3)-(42)=0

We multiply parentheses ..

(+x^2-3x-2x+6)-42=0

We get rid of parentheses

x^2-3x-2x+6-42=0

We add all the numbers together, and all the variables

x^2-5x-36=0

a = 1; b = -5; c = -36;
Δ = b2-4ac
Δ = -52-4·1·(-36)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*1}=\frac{18}{2}
=9
$