144=w(w+2)

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

144=w(w+2)

We move all terms to the left:

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


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

w(w+2)

We multiply parentheses

w^2+2w

Back to the equation:

-(w^2+2w)


We get rid of parentheses

-w^2-2w+144=0

We add all the numbers together, and all the variables

-1w^2-2w+144=0

a = -1; b = -2; c = +144;
Δ = b2-4ac
Δ = -22-4·(-1)·144
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{145}}{2*-1}=\frac{2-2\sqrt{145}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{145}}{2*-1}=\frac{2+2\sqrt{145}}{-2}
$