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X2-12X-81=0
We add all the numbers together, and all the variables
X^2-12X-81=0
a = 1; b = -12; c = -81;
Δ = b2-4ac
Δ = -122-4·1·(-81)
Δ = 468
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{13}}{2*1}=\frac{12-6\sqrt{13}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{13}}{2*1}=\frac{12+6\sqrt{13}}{2} $
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