x(x-8)=42

Solution for x(x-8)=42 equation:

x(x-8)=42

We move all terms to the left:

x(x-8)-(42)=0

We multiply parentheses

x^2-8x-42=0

a = 1; b = -8; c = -42;
Δ = b2-4ac
Δ = -82-4·1·(-42)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{58}}{2*1}=\frac{8-2\sqrt{58}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{58}}{2*1}=\frac{8+2\sqrt{58}}{2}
$