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4/7x-1/14=3/2x
We move all terms to the left:
4/7x-1/14-(3/2x)=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
4/7x-(+3/2x)-1/14=0
We get rid of parentheses
4/7x-3/2x-1/14=0
We calculate fractions
(-28x^2)/196x^2+112x/196x^2+(-294x)/196x^2=0
We multiply all the terms by the denominator
(-28x^2)+112x+(-294x)=0
We get rid of parentheses
-28x^2+112x-294x=0
We add all the numbers together, and all the variables
-28x^2-182x=0
a = -28; b = -182; c = 0;
Δ = b2-4ac
Δ = -1822-4·(-28)·0
Δ = 33124
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{33124}=182$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-182}{2*-28}=\frac{0}{-56} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+182}{2*-28}=\frac{364}{-56} =-6+1/2 $
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