72=w(w+18)

Solution for 72=w(w+18) equation:

72=w(w+18)

We move all terms to the left:

72-(w(w+18))=0


We calculate terms in parentheses: -(w(w+18)), so:

w(w+18)

We multiply parentheses

w^2+18w

Back to the equation:

-(w^2+18w)


We get rid of parentheses

-w^2-18w+72=0

We add all the numbers together, and all the variables

-1w^2-18w+72=0

a = -1; b = -18; c = +72;
Δ = b2-4ac
Δ = -182-4·(-1)·72
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*-1}=\frac{18-6\sqrt{17}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*-1}=\frac{18+6\sqrt{17}}{-2}
$