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1/2x+3=5/6x-1
We move all terms to the left:
1/2x+3-(5/6x-1)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 6x-1)!=0We get rid of parentheses
x∈R
1/2x-5/6x+1+3=0
We calculate fractions
6x/12x^2+(-10x)/12x^2+1+3=0
We add all the numbers together, and all the variables
6x/12x^2+(-10x)/12x^2+4=0
We multiply all the terms by the denominator
6x+(-10x)+4*12x^2=0
Wy multiply elements
48x^2+6x+(-10x)=0
We get rid of parentheses
48x^2+6x-10x=0
We add all the numbers together, and all the variables
48x^2-4x=0
a = 48; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·48·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*48}=\frac{0}{96} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*48}=\frac{8}{96} =1/12 $
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