x(x-24)=48(x+3)

Solution for x(x-24)=48(x+3) equation:

x(x-24)=48(x+3)

We move all terms to the left:

x(x-24)-(48(x+3))=0

We multiply parentheses

x^2-24x-(48(x+3))=0


We calculate terms in parentheses: -(48(x+3)), so:

48(x+3)

We multiply parentheses

48x+144

Back to the equation:

-(48x+144)


We get rid of parentheses

x^2-24x-48x-144=0

We add all the numbers together, and all the variables

x^2-72x-144=0

a = 1; b = -72; c = -144;
Δ = b2-4ac
Δ = -722-4·1·(-144)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{10}}{2*1}=\frac{72-24\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{10}}{2*1}=\frac{72+24\sqrt{10}}{2}
$