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x/2x+6x+2=34
We move all terms to the left:
x/2x+6x+2-(34)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
6x+x/2x-32=0
We multiply all the terms by the denominator
6x*2x+x-32*2x=0
We add all the numbers together, and all the variables
x+6x*2x-32*2x=0
Wy multiply elements
12x^2+x-64x=0
We add all the numbers together, and all the variables
12x^2-63x=0
a = 12; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·12·0
Δ = 3969
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{3969}=63$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*12}=\frac{0}{24} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*12}=\frac{126}{24} =5+1/4 $
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