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1/2x+3/5x+7=29
We move all terms to the left:
1/2x+3/5x+7-(29)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
1/2x+3/5x-22=0
We calculate fractions
5x/10x^2+6x/10x^2-22=0
We multiply all the terms by the denominator
5x+6x-22*10x^2=0
We add all the numbers together, and all the variables
11x-22*10x^2=0
Wy multiply elements
-220x^2+11x=0
a = -220; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-220)·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-220}=\frac{-22}{-440} =1/20 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-220}=\frac{0}{-440} =0 $
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