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4/3x+3x=27
We move all terms to the left:
4/3x+3x-(27)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
3x+4/3x-27=0
We multiply all the terms by the denominator
3x*3x-27*3x+4=0
Wy multiply elements
9x^2-81x+4=0
a = 9; b = -81; c = +4;
Δ = b2-4ac
Δ = -812-4·9·4
Δ = 6417
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6417}=\sqrt{9*713}=\sqrt{9}*\sqrt{713}=3\sqrt{713}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{713}}{2*9}=\frac{81-3\sqrt{713}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{713}}{2*9}=\frac{81+3\sqrt{713}}{18} $
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