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3/4x-2=-7+1/3x
We move all terms to the left:
3/4x-2-(-7+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
3/4x-(1/3x-7)-2=0
We get rid of parentheses
3/4x-1/3x+7-2=0
We calculate fractions
9x/12x^2+(-4x)/12x^2+7-2=0
We add all the numbers together, and all the variables
9x/12x^2+(-4x)/12x^2+5=0
We multiply all the terms by the denominator
9x+(-4x)+5*12x^2=0
Wy multiply elements
60x^2+9x+(-4x)=0
We get rid of parentheses
60x^2+9x-4x=0
We add all the numbers together, and all the variables
60x^2+5x=0
a = 60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·60·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*60}=\frac{-10}{120} =-1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*60}=\frac{0}{120} =0 $
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