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X^2-12X-216=0
a = 1; b = -12; c = -216;
Δ = b2-4ac
Δ = -122-4·1·(-216)
Δ = 1008
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{7}}{2*1}=\frac{12-12\sqrt{7}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{7}}{2*1}=\frac{12+12\sqrt{7}}{2} $
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