x(2x-6)=24

Solution for x(2x-6)=24 equation:

x(2x-6)=24

We move all terms to the left:

x(2x-6)-(24)=0

We multiply parentheses

2x^2-6x-24=0

a = 2; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·2·(-24)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{57}}{2*2}=\frac{6-2\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{57}}{2*2}=\frac{6+2\sqrt{57}}{4}
$