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1/3+7/2x-1/6=-1/3x-3
We move all terms to the left:
1/3+7/2x-1/6-(-1/3x-3)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x-3)!=0We get rid of parentheses
x∈R
7/2x+1/3x+3+1/3-1/6=0
We calculate fractions
(-54x^2)/324x^2+1134x/324x^2+72x/324x^2+72x/324x^2+3=0
We multiply all the terms by the denominator
(-54x^2)+1134x+72x+72x+3*324x^2=0
We add all the numbers together, and all the variables
(-54x^2)+1278x+3*324x^2=0
Wy multiply elements
(-54x^2)+972x^2+1278x=0
We get rid of parentheses
-54x^2+972x^2+1278x=0
We add all the numbers together, and all the variables
918x^2+1278x=0
a = 918; b = 1278; c = 0;
Δ = b2-4ac
Δ = 12782-4·918·0
Δ = 1633284
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{1633284}=1278$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1278)-1278}{2*918}=\frac{-2556}{1836} =-1+20/51 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1278)+1278}{2*918}=\frac{0}{1836} =0 $
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