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9x^2/3+4x^-2/3=27
We move all terms to the left:
9x^2/3+4x^-2/3-(27)=0
determiningTheFunctionDomain 9x^2/3+4x^-27-2/3=0
We add all the numbers together, and all the variables
9x^2/3+4x-27-2/3=0
We multiply all the terms by the denominator
9x^2+4x*3-2-27*3=0
We add all the numbers together, and all the variables
9x^2+4x*3-83=0
Wy multiply elements
9x^2+12x-83=0
a = 9; b = 12; c = -83;
Δ = b2-4ac
Δ = 122-4·9·(-83)
Δ = 3132
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3132}=\sqrt{36*87}=\sqrt{36}*\sqrt{87}=6\sqrt{87}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{87}}{2*9}=\frac{-12-6\sqrt{87}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{87}}{2*9}=\frac{-12+6\sqrt{87}}{18} $
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