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(2w-3)(w-3)=55
We move all terms to the left:
(2w-3)(w-3)-(55)=0
We multiply parentheses ..
(+2w^2-6w-3w+9)-55=0
We get rid of parentheses
2w^2-6w-3w+9-55=0
We add all the numbers together, and all the variables
2w^2-9w-46=0
a = 2; b = -9; c = -46;
Δ = b2-4ac
Δ = -92-4·2·(-46)
Δ = 449
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{449}}{2*2}=\frac{9-\sqrt{449}}{4} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{449}}{2*2}=\frac{9+\sqrt{449}}{4} $
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