288x+288(x+4)=x(x+4)

Solution for 288x+288(x+4)=x(x+4) equation:

288x+288(x+4)=x(x+4)

We move all terms to the left:

288x+288(x+4)-(x(x+4))=0

We multiply parentheses

288x+288x-(x(x+4))+1152=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We add all the numbers together, and all the variables

576x-(x^2+4x)+1152=0

We get rid of parentheses

-x^2+576x-4x+1152=0

We add all the numbers together, and all the variables

-1x^2+572x+1152=0

a = -1; b = 572; c = +1152;
Δ = b2-4ac
Δ = 5722-4·(-1)·1152
Δ = 331792
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:

$\sqrt{\Delta}=\sqrt{331792}=\sqrt{16*20737}=\sqrt{16}*\sqrt{20737}=4\sqrt{20737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(572)-4\sqrt{20737}}{2*-1}=\frac{-572-4\sqrt{20737}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(572)+4\sqrt{20737}}{2*-1}=\frac{-572+4\sqrt{20737}}{-2}
$