X(x-8)=67

Solution for X(x-8)=67 equation:

X(X-8)=67

We move all terms to the left:

X(X-8)-(67)=0

We multiply parentheses

X^2-8X-67=0

a = 1; b = -8; c = -67;
Δ = b2-4ac
Δ = -82-4·1·(-67)
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{83}}{2*1}=\frac{8-2\sqrt{83}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{83}}{2*1}=\frac{8+2\sqrt{83}}{2}
$