144x+144(x+2)=(x)(x+2)

Solution for 144x+144(x+2)=(x)(x+2) equation:

144x+144(x+2)=(x)(x+2)

We move all terms to the left:

144x+144(x+2)-((x)(x+2))=0

We multiply parentheses

144x+144x-(x(x+2))+288=0


We calculate terms in parentheses: -(x(x+2)), so:

x(x+2)

We multiply parentheses

x^2+2x

Back to the equation:

-(x^2+2x)


We add all the numbers together, and all the variables

288x-(x^2+2x)+288=0

We get rid of parentheses

-x^2+288x-2x+288=0

We add all the numbers together, and all the variables

-1x^2+286x+288=0

a = -1; b = 286; c = +288;
Δ = b2-4ac
Δ = 2862-4·(-1)·288
Δ = 82948
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:

$\sqrt{\Delta}=\sqrt{82948}=\sqrt{4*20737}=\sqrt{4}*\sqrt{20737}=2\sqrt{20737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(286)-2\sqrt{20737}}{2*-1}=\frac{-286-2\sqrt{20737}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(286)+2\sqrt{20737}}{2*-1}=\frac{-286+2\sqrt{20737}}{-2}
$