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1/2x+5=1/3x+10
We move all terms to the left:
1/2x+5-(1/3x+10)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x+10)!=0We get rid of parentheses
x∈R
1/2x-1/3x-10+5=0
We calculate fractions
3x/6x^2+(-2x)/6x^2-10+5=0
We add all the numbers together, and all the variables
3x/6x^2+(-2x)/6x^2-5=0
We multiply all the terms by the denominator
3x+(-2x)-5*6x^2=0
Wy multiply elements
-30x^2+3x+(-2x)=0
We get rid of parentheses
-30x^2+3x-2x=0
We add all the numbers together, and all the variables
-30x^2+x=0
a = -30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-30)·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-30}=\frac{-2}{-60} =1/30 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-30}=\frac{0}{-60} =0 $
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