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27x^2-18x-625=0
a = 27; b = -18; c = -625;
Δ = b2-4ac
Δ = -182-4·27·(-625)
Δ = 67824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{67824}=\sqrt{144*471}=\sqrt{144}*\sqrt{471}=12\sqrt{471}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12\sqrt{471}}{2*27}=\frac{18-12\sqrt{471}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{471}}{2*27}=\frac{18+12\sqrt{471}}{54} $
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