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17+4x/10x+5=2/3x-1
We move all terms to the left:
17+4x/10x+5-(2/3x-1)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
Domain of the equation: 3x-1)!=0We add all the numbers together, and all the variables
x∈R
4x/10x-(2/3x-1)+22=0
We get rid of parentheses
4x/10x-2/3x+1+22=0
We calculate fractions
12x^2/30x^2+(-20x)/30x^2+1+22=0
We add all the numbers together, and all the variables
12x^2/30x^2+(-20x)/30x^2+23=0
We multiply all the terms by the denominator
12x^2+(-20x)+23*30x^2=0
Wy multiply elements
12x^2+690x^2+(-20x)=0
We get rid of parentheses
12x^2+690x^2-20x=0
We add all the numbers together, and all the variables
702x^2-20x=0
a = 702; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·702·0
Δ = 400
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{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*702}=\frac{0}{1404} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*702}=\frac{40}{1404} =10/351 $
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