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2/3x+8=-10-1/2x
We move all terms to the left:
2/3x+8-(-10-1/2x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(-1/2x-10)+8=0
We get rid of parentheses
2/3x+1/2x+10+8=0
We calculate fractions
4x/6x^2+3x/6x^2+10+8=0
We add all the numbers together, and all the variables
4x/6x^2+3x/6x^2+18=0
We multiply all the terms by the denominator
4x+3x+18*6x^2=0
We add all the numbers together, and all the variables
7x+18*6x^2=0
Wy multiply elements
108x^2+7x=0
a = 108; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·108·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*108}=\frac{-14}{216} =-7/108 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*108}=\frac{0}{216} =0 $
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