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2/4x+1=5/3x-4
We move all terms to the left:
2/4x+1-(5/3x-4)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x-4)!=0We get rid of parentheses
x∈R
2/4x-5/3x+4+1=0
We calculate fractions
6x/12x^2+(-20x)/12x^2+4+1=0
We add all the numbers together, and all the variables
6x/12x^2+(-20x)/12x^2+5=0
We multiply all the terms by the denominator
6x+(-20x)+5*12x^2=0
Wy multiply elements
60x^2+6x+(-20x)=0
We get rid of parentheses
60x^2+6x-20x=0
We add all the numbers together, and all the variables
60x^2-14x=0
a = 60; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·60·0
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*60}=\frac{0}{120} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*60}=\frac{28}{120} =7/30 $
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