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2w^2-11w-15=55
We move all terms to the left:
2w^2-11w-15-(55)=0
We add all the numbers together, and all the variables
2w^2-11w-70=0
a = 2; b = -11; c = -70;
Δ = b2-4ac
Δ = -112-4·2·(-70)
Δ = 681
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{-(-11)-\sqrt{681}}{2*2}=\frac{11-\sqrt{681}}{4} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{681}}{2*2}=\frac{11+\sqrt{681}}{4} $
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