X(x+8)=106

Solution for X(x+8)=106 equation:

X(X+8)=106

We move all terms to the left:

X(X+8)-(106)=0

We multiply parentheses

X^2+8X-106=0

a = 1; b = 8; c = -106;
Δ = b2-4ac
Δ = 82-4·1·(-106)
Δ = 488
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:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{122}}{2*1}=\frac{-8-2\sqrt{122}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{122}}{2*1}=\frac{-8+2\sqrt{122}}{2}
$