X2-12x=27

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Solution for X2-12x=27 equation:



X2-12X=27
We move all terms to the left:
X2-12X-(27)=0
We add all the numbers together, and all the variables
X^2-12X-27=0
a = 1; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·1·(-27)
Δ = 252
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:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{7}}{2*1}=\frac{12-6\sqrt{7}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{7}}{2*1}=\frac{12+6\sqrt{7}}{2} $

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