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1/4x-4=3-1/3x
We move all terms to the left:
1/4x-4-(3-1/3x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/4x-(-1/3x+3)-4=0
We get rid of parentheses
1/4x+1/3x-3-4=0
We calculate fractions
3x/12x^2+4x/12x^2-3-4=0
We add all the numbers together, and all the variables
3x/12x^2+4x/12x^2-7=0
We multiply all the terms by the denominator
3x+4x-7*12x^2=0
We add all the numbers together, and all the variables
7x-7*12x^2=0
Wy multiply elements
-84x^2+7x=0
a = -84; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-84)·0
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-84}=\frac{-14}{-168} =1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-84}=\frac{0}{-168} =0 $
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