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6x+(35/x)=29
We move all terms to the left:
6x+(35/x)-(29)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
6x+(+35/x)-29=0
We get rid of parentheses
6x+35/x-29=0
We multiply all the terms by the denominator
6x*x-29*x+35=0
We add all the numbers together, and all the variables
-29x+6x*x+35=0
Wy multiply elements
6x^2-29x+35=0
a = 6; b = -29; c = +35;
Δ = b2-4ac
Δ = -292-4·6·35
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-1}{2*6}=\frac{28}{12} =2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+1}{2*6}=\frac{30}{12} =2+1/2 $
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