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1/10x+15=15/100x+10
We move all terms to the left:
1/10x+15-(15/100x+10)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
Domain of the equation: 100x+10)!=0We get rid of parentheses
x∈R
1/10x-15/100x-10+15=0
We calculate fractions
100x/1000x^2+(-150x)/1000x^2-10+15=0
We add all the numbers together, and all the variables
100x/1000x^2+(-150x)/1000x^2+5=0
We multiply all the terms by the denominator
100x+(-150x)+5*1000x^2=0
Wy multiply elements
5000x^2+100x+(-150x)=0
We get rid of parentheses
5000x^2+100x-150x=0
We add all the numbers together, and all the variables
5000x^2-50x=0
a = 5000; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·5000·0
Δ = 2500
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{2500}=50$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*5000}=\frac{0}{10000} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*5000}=\frac{100}{10000} =1/100 $
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