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1/4x+5/3-4=2-1/2x
We move all terms to the left:
1/4x+5/3-4-(2-1/2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/4x-(-1/2x+2)-4+5/3=0
We get rid of parentheses
1/4x+1/2x-2-4+5/3=0
We calculate fractions
80x^2/72x^2+18x/72x^2+36x/72x^2-2-4=0
We add all the numbers together, and all the variables
80x^2/72x^2+18x/72x^2+36x/72x^2-6=0
We multiply all the terms by the denominator
80x^2+18x+36x-6*72x^2=0
We add all the numbers together, and all the variables
80x^2+54x-6*72x^2=0
Wy multiply elements
80x^2-432x^2+54x=0
We add all the numbers together, and all the variables
-352x^2+54x=0
a = -352; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-352)·0
Δ = 2916
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{2916}=54$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-352}=\frac{-108}{-704} =27/176 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-352}=\frac{0}{-704} =0 $
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