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3/4x+2/3=7/6x
We move all terms to the left:
3/4x+2/3-(7/6x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 6x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/4x-(+7/6x)+2/3=0
We get rid of parentheses
3/4x-7/6x+2/3=0
We calculate fractions
288x^2/216x^2+162x/216x^2+(-252x)/216x^2=0
We multiply all the terms by the denominator
288x^2+162x+(-252x)=0
We get rid of parentheses
288x^2+162x-252x=0
We add all the numbers together, and all the variables
288x^2-90x=0
a = 288; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·288·0
Δ = 8100
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{8100}=90$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*288}=\frac{0}{576} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*288}=\frac{180}{576} =5/16 $
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