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5/6x+8=1/2x
We move all terms to the left:
5/6x+8-(1/2x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/6x-(+1/2x)+8=0
We get rid of parentheses
5/6x-1/2x+8=0
We calculate fractions
10x/12x^2+(-6x)/12x^2+8=0
We multiply all the terms by the denominator
10x+(-6x)+8*12x^2=0
Wy multiply elements
96x^2+10x+(-6x)=0
We get rid of parentheses
96x^2+10x-6x=0
We add all the numbers together, and all the variables
96x^2+4x=0
a = 96; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·96·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*96}=\frac{-8}{192} =-1/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*96}=\frac{0}{192} =0 $
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