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X^2+1.66667X-0.66667=0
a = 1; b = 1.66667; c = -0.66667;
Δ = b2-4ac
Δ = 1.666672-4·1·(-0.66667)
Δ = 5.4444688889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.66667)-\sqrt{5.4444688889}}{2*1}=\frac{-1.66667-\sqrt{5.4444688889}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.66667)+\sqrt{5.4444688889}}{2*1}=\frac{-1.66667+\sqrt{5.4444688889}}{2} $
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