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2(4+9w)w=4
We move all terms to the left:
2(4+9w)w-(4)=0
We add all the numbers together, and all the variables
2(9w+4)w-4=0
We multiply parentheses
18w^2+8w-4=0
a = 18; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·18·(-4)
Δ = 352
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*18}=\frac{-8-4\sqrt{22}}{36} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*18}=\frac{-8+4\sqrt{22}}{36} $
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