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3/4x+1/2=1/3x+2
We move all terms to the left:
3/4x+1/2-(1/3x+2)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x+2)!=0We get rid of parentheses
x∈R
3/4x-1/3x-2+1/2=0
We calculate fractions
36x^2/48x^2+36x/48x^2+(-16x)/48x^2-2=0
We multiply all the terms by the denominator
36x^2+36x+(-16x)-2*48x^2=0
Wy multiply elements
36x^2-96x^2+36x+(-16x)=0
We get rid of parentheses
36x^2-96x^2+36x-16x=0
We add all the numbers together, and all the variables
-60x^2+20x=0
a = -60; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-60)·0
Δ = 400
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{400}=20x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-60}=\frac{-40}{-120} =1/3x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-60}=\frac{0}{-120} =0
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