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2/3x-1=6/7x
We move all terms to the left:
2/3x-1-(6/7x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 7x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(+6/7x)-1=0
We get rid of parentheses
2/3x-6/7x-1=0
We calculate fractions
14x/21x^2+(-18x)/21x^2-1=0
We multiply all the terms by the denominator
14x+(-18x)-1*21x^2=0
Wy multiply elements
-21x^2+14x+(-18x)=0
We get rid of parentheses
-21x^2+14x-18x=0
We add all the numbers together, and all the variables
-21x^2-4x=0
a = -21; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-21)·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-21}=\frac{0}{-42} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-21}=\frac{8}{-42} =-4/21 $
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