x(x+8)=172

Solution for x(x+8)=172 equation:

x(x+8)=172

We move all terms to the left:

x(x+8)-(172)=0

We multiply parentheses

x^2+8x-172=0

a = 1; b = 8; c = -172;
Δ = b2-4ac
Δ = 82-4·1·(-172)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{47}}{2*1}=\frac{-8-4\sqrt{47}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{47}}{2*1}=\frac{-8+4\sqrt{47}}{2}
$