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171x^2-171x+1=0
a = 171; b = -171; c = +1;
Δ = b2-4ac
Δ = -1712-4·171·1
Δ = 28557
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28557}=\sqrt{9*3173}=\sqrt{9}*\sqrt{3173}=3\sqrt{3173}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-171)-3\sqrt{3173}}{2*171}=\frac{171-3\sqrt{3173}}{342} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-171)+3\sqrt{3173}}{2*171}=\frac{171+3\sqrt{3173}}{342} $
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