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2/3x+5=-2/6x+4
We move all terms to the left:
2/3x+5-(-2/6x+4)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x+4)!=0We get rid of parentheses
x∈R
2/3x+2/6x-4+5=0
We calculate fractions
12x/18x^2+6x/18x^2-4+5=0
We add all the numbers together, and all the variables
12x/18x^2+6x/18x^2+1=0
We multiply all the terms by the denominator
12x+6x+1*18x^2=0
We add all the numbers together, and all the variables
18x+1*18x^2=0
Wy multiply elements
18x^2+18x=0
a = 18; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·18·0
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*18}=\frac{-36}{36} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*18}=\frac{0}{36} =0 $
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