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11x-x^2=6
We move all terms to the left:
11x-x^2-(6)=0
We add all the numbers together, and all the variables
-1x^2+11x-6=0
a = -1; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-1)·(-6)
Δ = 97
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{97}}{2*-1}=\frac{-11-\sqrt{97}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{97}}{2*-1}=\frac{-11+\sqrt{97}}{-2} $
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