2w(w-15)=72

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

2w(w-15)=72

We move all terms to the left:

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

We multiply 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}
$