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9x^2-x=2
We move all terms to the left:
9x^2-x-(2)=0
We add all the numbers together, and all the variables
9x^2-1x-2=0
a = 9; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·9·(-2)
Δ = 73
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{-(-1)-\sqrt{73}}{2*9}=\frac{1-\sqrt{73}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*9}=\frac{1+\sqrt{73}}{18} $
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