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2/4x-6=1/5x
We move all terms to the left:
2/4x-6-(1/5x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/4x-(+1/5x)-6=0
We get rid of parentheses
2/4x-1/5x-6=0
We calculate fractions
10x/20x^2+(-4x)/20x^2-6=0
We multiply all the terms by the denominator
10x+(-4x)-6*20x^2=0
Wy multiply elements
-120x^2+10x+(-4x)=0
We get rid of parentheses
-120x^2+10x-4x=0
We add all the numbers together, and all the variables
-120x^2+6x=0
a = -120; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-120)·0
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-120}=\frac{-12}{-240} =1/20 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-120}=\frac{0}{-240} =0 $
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