4w^2+18w=72

Solution for 4w^2+18w=72 equation:

4w^2+18w=72

We move all terms to the left:

4w^2+18w-(72)=0

a = 4; b = 18; c = -72;
Δ = b2-4ac
Δ = 182-4·4·(-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{-(18)-6\sqrt{41}}{2*4}=\frac{-18-6\sqrt{41}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{41}}{2*4}=\frac{-18+6\sqrt{41}}{8}
$