x(x+8)=136

Solution for x(x+8)=136 equation:

x(x+8)=136

We move all terms to the left:

x(x+8)-(136)=0

We multiply parentheses

x^2+8x-136=0

a = 1; b = 8; c = -136;
Δ = b2-4ac
Δ = 82-4·1·(-136)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{38}}{2*1}=\frac{-8-4\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{38}}{2*1}=\frac{-8+4\sqrt{38}}{2}
$