x(x+8)=(8)(6)

Solution for x(x+8)=(8)(6) equation:

x(x+8)=(8)(6)

We move all terms to the left:

x(x+8)-((8)(6))=0

determiningTheFunctionDomain
x(x+8)-86=0

We multiply parentheses

x^2+8x-86=0

a = 1; b = 8; c = -86;
Δ = b2-4ac
Δ = 82-4·1·(-86)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{102}}{2*1}=\frac{-8-2\sqrt{102}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{102}}{2*1}=\frac{-8+2\sqrt{102}}{2}
$