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-24+11x=x^2
We move all terms to the left:
-24+11x-(x^2)=0
determiningTheFunctionDomain -x^2+11x-24=0
We add all the numbers together, and all the variables
-1x^2+11x-24=0
a = -1; b = 11; c = -24;
Δ = b2-4ac
Δ = 112-4·(-1)·(-24)
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*-1}=\frac{-16}{-2} =+8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-1}=\frac{-6}{-2} =+3 $
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