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

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

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

We move all terms to the left:

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

determiningTheFunctionDomain
x(x+8)-68=0

We multiply parentheses

x^2+8x-68=0

a = 1; b = 8; c = -68;
Δ = b2-4ac
Δ = 82-4·1·(-68)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{21}}{2*1}=\frac{-8-4\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{21}}{2*1}=\frac{-8+4\sqrt{21}}{2}
$