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18+1/5x=16+7/10x
We move all terms to the left:
18+1/5x-(16+7/10x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/5x-(7/10x+16)+18=0
We get rid of parentheses
1/5x-7/10x-16+18=0
We calculate fractions
10x/50x^2+(-35x)/50x^2-16+18=0
We add all the numbers together, and all the variables
10x/50x^2+(-35x)/50x^2+2=0
We multiply all the terms by the denominator
10x+(-35x)+2*50x^2=0
Wy multiply elements
100x^2+10x+(-35x)=0
We get rid of parentheses
100x^2+10x-35x=0
We add all the numbers together, and all the variables
100x^2-25x=0
a = 100; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·100·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*100}=\frac{0}{200} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*100}=\frac{50}{200} =1/4 $
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