x(x-2)=47

Solution for x(x-2)=47 equation:

x(x-2)=47

We move all terms to the left:

x(x-2)-(47)=0

We multiply parentheses

x^2-2x-47=0

a = 1; b = -2; c = -47;
Δ = b2-4ac
Δ = -22-4·1·(-47)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{3}}{2*1}=\frac{2-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{3}}{2*1}=\frac{2+8\sqrt{3}}{2}
$