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54-2w^2-3w=0
a = -2; b = -3; c = +54;
Δ = b2-4ac
Δ = -32-4·(-2)·54
Δ = 441
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{441}=21$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*-2}=\frac{-18}{-4} =4+1/2 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*-2}=\frac{24}{-4} =-6 $
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