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9x^2+3x=1/81
We move all terms to the left:
9x^2+3x-(1/81)=0
We add all the numbers together, and all the variables
9x^2+3x-(+1/81)=0
We get rid of parentheses
9x^2+3x-1/81=0
We multiply all the terms by the denominator
9x^2*81+3x*81-1=0
Wy multiply elements
729x^2+243x-1=0
a = 729; b = 243; c = -1;
Δ = b2-4ac
Δ = 2432-4·729·(-1)
Δ = 61965
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{61965}=\sqrt{729*85}=\sqrt{729}*\sqrt{85}=27\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(243)-27\sqrt{85}}{2*729}=\frac{-243-27\sqrt{85}}{1458} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(243)+27\sqrt{85}}{2*729}=\frac{-243+27\sqrt{85}}{1458} $
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