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2/3x-5=6-1/4x
We move all terms to the left:
2/3x-5-(6-1/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(-1/4x+6)-5=0
We get rid of parentheses
2/3x+1/4x-6-5=0
We calculate fractions
8x/12x^2+3x/12x^2-6-5=0
We add all the numbers together, and all the variables
8x/12x^2+3x/12x^2-11=0
We multiply all the terms by the denominator
8x+3x-11*12x^2=0
We add all the numbers together, and all the variables
11x-11*12x^2=0
Wy multiply elements
-132x^2+11x=0
a = -132; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-132)·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}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-132}=\frac{-22}{-264} =1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-132}=\frac{0}{-264} =0 $
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