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7x(x-1)=1
We move all terms to the left:
7x(x-1)-(1)=0
We multiply parentheses
7x^2-7x-1=0
a = 7; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·7·(-1)
Δ = 77
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{-(-7)-\sqrt{77}}{2*7}=\frac{7-\sqrt{77}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{77}}{2*7}=\frac{7+\sqrt{77}}{14} $
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