x(x-3)=65

Solution for x(x-3)=65 equation:

x(x-3)=65

We move all terms to the left:

x(x-3)-(65)=0

We multiply parentheses

x^2-3x-65=0

a = 1; b = -3; c = -65;
Δ = b2-4ac
Δ = -32-4·1·(-65)
Δ = 269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{269}}{2*1}=\frac{3-\sqrt{269}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{269}}{2*1}=\frac{3+\sqrt{269}}{2}
$