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27x^2-6x-432=0
a = 27; b = -6; c = -432;
Δ = b2-4ac
Δ = -62-4·27·(-432)
Δ = 46692
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{46692}=\sqrt{36*1297}=\sqrt{36}*\sqrt{1297}=6\sqrt{1297}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{1297}}{2*27}=\frac{6-6\sqrt{1297}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{1297}}{2*27}=\frac{6+6\sqrt{1297}}{54} $
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