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1/3x+3=266/18x-23
We move all terms to the left:
1/3x+3-(266/18x-23)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 18x-23)!=0We get rid of parentheses
x∈R
1/3x-266/18x+23+3=0
We calculate fractions
18x/54x^2+(-798x)/54x^2+23+3=0
We add all the numbers together, and all the variables
18x/54x^2+(-798x)/54x^2+26=0
We multiply all the terms by the denominator
18x+(-798x)+26*54x^2=0
Wy multiply elements
1404x^2+18x+(-798x)=0
We get rid of parentheses
1404x^2+18x-798x=0
We add all the numbers together, and all the variables
1404x^2-780x=0
a = 1404; b = -780; c = 0;
Δ = b2-4ac
Δ = -7802-4·1404·0
Δ = 608400
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{608400}=780$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-780)-780}{2*1404}=\frac{0}{2808} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-780)+780}{2*1404}=\frac{1560}{2808} =5/9 $
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