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2/4x-2=-6+5/12x
We move all terms to the left:
2/4x-2-(-6+5/12x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 12x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/4x-(5/12x-6)-2=0
We get rid of parentheses
2/4x-5/12x+6-2=0
We calculate fractions
24x/48x^2+(-20x)/48x^2+6-2=0
We add all the numbers together, and all the variables
24x/48x^2+(-20x)/48x^2+4=0
We multiply all the terms by the denominator
24x+(-20x)+4*48x^2=0
Wy multiply elements
192x^2+24x+(-20x)=0
We get rid of parentheses
192x^2+24x-20x=0
We add all the numbers together, and all the variables
192x^2+4x=0
a = 192; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·192·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*192}=\frac{-8}{384} =-1/48 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*192}=\frac{0}{384} =0 $
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