x(x-8)=144

Solution for x(x-8)=144 equation:

x(x-8)=144

We move all terms to the left:

x(x-8)-(144)=0

We multiply parentheses

x^2-8x-144=0

a = 1; b = -8; c = -144;
Δ = b2-4ac
Δ = -82-4·1·(-144)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{10}}{2*1}=\frac{8-8\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{10}}{2*1}=\frac{8+8\sqrt{10}}{2}
$