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1/4x+12=1/6x+2
We move all terms to the left:
1/4x+12-(1/6x+2)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 6x+2)!=0We get rid of parentheses
x∈R
1/4x-1/6x-2+12=0
We calculate fractions
6x/24x^2+(-4x)/24x^2-2+12=0
We add all the numbers together, and all the variables
6x/24x^2+(-4x)/24x^2+10=0
We multiply all the terms by the denominator
6x+(-4x)+10*24x^2=0
Wy multiply elements
240x^2+6x+(-4x)=0
We get rid of parentheses
240x^2+6x-4x=0
We add all the numbers together, and all the variables
240x^2+2x=0
a = 240; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·240·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*240}=\frac{-4}{480} =-1/120 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*240}=\frac{0}{480} =0 $
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