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81x^2-102x+30=0
a = 81; b = -102; c = +30;
Δ = b2-4ac
Δ = -1022-4·81·30
Δ = 684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{19}}{2*81}=\frac{102-6\sqrt{19}}{162} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{19}}{2*81}=\frac{102+6\sqrt{19}}{162} $
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