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4/9x+1/2x=34
We move all terms to the left:
4/9x+1/2x-(34)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 2x!=0We calculate fractions
x!=0/2
x!=0
x∈R
8x/18x^2+9x/18x^2-34=0
We multiply all the terms by the denominator
8x+9x-34*18x^2=0
We add all the numbers together, and all the variables
17x-34*18x^2=0
Wy multiply elements
-612x^2+17x=0
a = -612; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-612)·0
Δ = 289
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-612}=\frac{-34}{-1224} =1/36 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-612}=\frac{0}{-1224} =0 $
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