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1/5x+30=-1/2x-5
We move all terms to the left:
1/5x+30-(-1/2x-5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x-5)!=0We get rid of parentheses
x∈R
1/5x+1/2x+5+30=0
We calculate fractions
2x/10x^2+5x/10x^2+5+30=0
We add all the numbers together, and all the variables
2x/10x^2+5x/10x^2+35=0
We multiply all the terms by the denominator
2x+5x+35*10x^2=0
We add all the numbers together, and all the variables
7x+35*10x^2=0
Wy multiply elements
350x^2+7x=0
a = 350; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·350·0
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*350}=\frac{-14}{700} =-1/50 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*350}=\frac{0}{700} =0 $
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