X(n-6)=42

Solution for X(n-6)=42 equation:

X(X-6)=42

We move all terms to the left:

X(X-6)-(42)=0

We multiply parentheses

X^2-6X-42=0

a = 1; b = -6; c = -42;
Δ = b2-4ac
Δ = -62-4·1·(-42)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{51}}{2*1}=\frac{6-2\sqrt{51}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{51}}{2*1}=\frac{6+2\sqrt{51}}{2}
$