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6x+27=x^2
We move all terms to the left:
6x+27-(x^2)=0
determiningTheFunctionDomain -x^2+6x+27=0
We add all the numbers together, and all the variables
-1x^2+6x+27=0
a = -1; b = 6; c = +27;
Δ = b2-4ac
Δ = 62-4·(-1)·27
Δ = 144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*-1}=\frac{-18}{-2} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*-1}=\frac{6}{-2} =-3 $
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