x(x-3)=547

Solution for x(x-3)=547 equation:

x(x-3)=547

We move all terms to the left:

x(x-3)-(547)=0

We multiply parentheses

x^2-3x-547=0

a = 1; b = -3; c = -547;
Δ = b2-4ac
Δ = -32-4·1·(-547)
Δ = 2197
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:

$\sqrt{\Delta}=\sqrt{2197}=\sqrt{169*13}=\sqrt{169}*\sqrt{13}=13\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13\sqrt{13}}{2*1}=\frac{3-13\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13\sqrt{13}}{2*1}=\frac{3+13\sqrt{13}}{2}
$