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3/7x+1/10=1/2x
We move all terms to the left:
3/7x+1/10-(1/2x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/7x-(+1/2x)+1/10=0
We get rid of parentheses
3/7x-1/2x+1/10=0
We calculate fractions
28x^2/140x^2+60x/140x^2+(-70x)/140x^2=0
We multiply all the terms by the denominator
28x^2+60x+(-70x)=0
We get rid of parentheses
28x^2+60x-70x=0
We add all the numbers together, and all the variables
28x^2-10x=0
a = 28; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·28·0
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*28}=\frac{0}{56} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*28}=\frac{20}{56} =5/14 $
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