18-2w=4w2

Solution for 18-2w=4w2 equation:

18-2w=4w^2

We move all terms to the left:

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

determiningTheFunctionDomain
-4w^2-2w+18=0

a = -4; b = -2; c = +18;
Δ = b2-4ac
Δ = -22-4·(-4)·18
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{73}}{2*-4}=\frac{2-2\sqrt{73}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{73}}{2*-4}=\frac{2+2\sqrt{73}}{-8}
$