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1/3x+10=-1/2x+5
We move all terms to the left:
1/3x+10-(-1/2x+5)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x+5)!=0We get rid of parentheses
x∈R
1/3x+1/2x-5+10=0
We calculate fractions
2x/6x^2+3x/6x^2-5+10=0
We add all the numbers together, and all the variables
2x/6x^2+3x/6x^2+5=0
We multiply all the terms by the denominator
2x+3x+5*6x^2=0
We add all the numbers together, and all the variables
5x+5*6x^2=0
Wy multiply elements
30x^2+5x=0
a = 30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·30·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*30}=\frac{-10}{60} =-1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*30}=\frac{0}{60} =0 $
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