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x^2-27x=243=0
We move all terms to the left:
x^2-27x-(243)=0
a = 1; b = -27; c = -243;
Δ = b2-4ac
Δ = -272-4·1·(-243)
Δ = 1701
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{21}}{2*1}=\frac{27-9\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{21}}{2*1}=\frac{27+9\sqrt{21}}{2} $
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