72=2w(w-15)

Solution for 72=2w(w-15) equation:

72=2w(w-15)

We move all terms to the left:

72-(2w(w-15))=0


We calculate terms in parentheses: -(2w(w-15)), so:

2w(w-15)

We multiply parentheses

2w^2-30w

Back to the equation:

-(2w^2-30w)


We get rid of parentheses

-2w^2+30w+72=0

a = -2; b = 30; c = +72;
Δ = b2-4ac
Δ = 302-4·(-2)·72
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{41}}{2*-2}=\frac{-30-6\sqrt{41}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{41}}{2*-2}=\frac{-30+6\sqrt{41}}{-4}
$