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11x^2-9x+1=6x^2
We move all terms to the left:
11x^2-9x+1-(6x^2)=0
determiningTheFunctionDomain 11x^2-6x^2-9x+1=0
We add all the numbers together, and all the variables
5x^2-9x+1=0
a = 5; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·5·1
Δ = 61
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{-(-9)-\sqrt{61}}{2*5}=\frac{9-\sqrt{61}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{61}}{2*5}=\frac{9+\sqrt{61}}{10} $
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