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9x^2-18x+11=6
We move all terms to the left:
9x^2-18x+11-(6)=0
We add all the numbers together, and all the variables
9x^2-18x+5=0
a = 9; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·9·5
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*9}=\frac{6}{18} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*9}=\frac{30}{18} =1+2/3 $
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