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2/x-4=5/6x-7
We move all terms to the left:
2/x-4-(5/6x-7)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 6x-7)!=0We get rid of parentheses
x∈R
2/x-5/6x+7-4=0
We calculate fractions
12x/6x^2+(-5x)/6x^2+7-4=0
We add all the numbers together, and all the variables
12x/6x^2+(-5x)/6x^2+3=0
We multiply all the terms by the denominator
12x+(-5x)+3*6x^2=0
Wy multiply elements
18x^2+12x+(-5x)=0
We get rid of parentheses
18x^2+12x-5x=0
We add all the numbers together, and all the variables
18x^2+7x=0
a = 18; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·18·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*18}=\frac{-14}{36} =-7/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*18}=\frac{0}{36} =0 $
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