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X(X-1)=0.67
We move all terms to the left:
X(X-1)-(0.67)=0
We add all the numbers together, and all the variables
X(X-1)-0.67=0
We multiply parentheses
X^2-1X-0.67=0
a = 1; b = -1; c = -0.67;
Δ = b2-4ac
Δ = -12-4·1·(-0.67)
Δ = 3.68
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)-\sqrt{3.68}}{2*1}=\frac{1-\sqrt{3.68}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3.68}}{2*1}=\frac{1+\sqrt{3.68}}{2} $
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