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1/10x-11=3/5x
We move all terms to the left:
1/10x-11-(3/5x)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/10x-(+3/5x)-11=0
We get rid of parentheses
1/10x-3/5x-11=0
We calculate fractions
5x/50x^2+(-30x)/50x^2-11=0
We multiply all the terms by the denominator
5x+(-30x)-11*50x^2=0
Wy multiply elements
-550x^2+5x+(-30x)=0
We get rid of parentheses
-550x^2+5x-30x=0
We add all the numbers together, and all the variables
-550x^2-25x=0
a = -550; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-550)·0
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-550}=\frac{0}{-1100} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-550}=\frac{50}{-1100} =-1/22 $
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