x(x-30)=240

Solution for x(x-30)=240 equation:

x(x-30)=240

We move all terms to the left:

x(x-30)-(240)=0

We multiply parentheses

x^2-30x-240=0

a = 1; b = -30; c = -240;
Δ = b2-4ac
Δ = -302-4·1·(-240)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{465}}{2*1}=\frac{30-2\sqrt{465}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{465}}{2*1}=\frac{30+2\sqrt{465}}{2}
$