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2/3x+1/4x=2
We move all terms to the left:
2/3x+1/4x-(2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x!=0We calculate fractions
x!=0/4
x!=0
x∈R
8x/12x^2+3x/12x^2-2=0
We multiply all the terms by the denominator
8x+3x-2*12x^2=0
We add all the numbers together, and all the variables
11x-2*12x^2=0
Wy multiply elements
-24x^2+11x=0
a = -24; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-24)·0
Δ = 121
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{121}=11x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-24}=\frac{-22}{-48} =11/24x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-24}=\frac{0}{-48} =0
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