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3/7-11/21x-1=2/3x
We move all terms to the left:
3/7-11/21x-1-(2/3x)=0
Domain of the equation: 21x!=0
x!=0/21
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-11/21x-(+2/3x)-1+3/7=0
We get rid of parentheses
-11/21x-2/3x-1+3/7=0
We calculate fractions
567x^2/3087x^2+(-1617x)/3087x^2+(-2058x)/3087x^2-1=0
We multiply all the terms by the denominator
567x^2+(-1617x)+(-2058x)-1*3087x^2=0
Wy multiply elements
567x^2-3087x^2+(-1617x)+(-2058x)=0
We get rid of parentheses
567x^2-3087x^2-1617x-2058x=0
We add all the numbers together, and all the variables
-2520x^2-3675x=0
a = -2520; b = -3675; c = 0;
Δ = b2-4ac
Δ = -36752-4·(-2520)·0
Δ = 13505625
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{13505625}=3675$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3675)-3675}{2*-2520}=\frac{0}{-5040} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3675)+3675}{2*-2520}=\frac{7350}{-5040} =-1+11/24 $
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