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3/5x+1/4=7/20x
We move all terms to the left:
3/5x+1/4-(7/20x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 20x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/5x-(+7/20x)+1/4=0
We get rid of parentheses
3/5x-7/20x+1/4=0
We calculate fractions
200x^2/1600x^2+960x/1600x^2+(-560x)/1600x^2=0
We multiply all the terms by the denominator
200x^2+960x+(-560x)=0
We get rid of parentheses
200x^2+960x-560x=0
We add all the numbers together, and all the variables
200x^2+400x=0
a = 200; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·200·0
Δ = 160000
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{160000}=400$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*200}=\frac{-800}{400} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*200}=\frac{0}{400} =0 $
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