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11=6x-0.5x^2
We move all terms to the left:
11-(6x-0.5x^2)=0
We get rid of parentheses
0.5x^2-6x+11=0
a = 0.5; b = -6; c = +11;
Δ = b2-4ac
Δ = -62-4·0.5·11
Δ = 14
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{-(-6)-\sqrt{14}}{2*0.5}=\frac{6-\sqrt{14}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{14}}{2*0.5}=\frac{6+\sqrt{14}}{1} $
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