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2/3x-6=28-3/4x
We move all terms to the left:
2/3x-6-(28-3/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(-3/4x+28)-6=0
We get rid of parentheses
2/3x+3/4x-28-6=0
We calculate fractions
8x/12x^2+9x/12x^2-28-6=0
We add all the numbers together, and all the variables
8x/12x^2+9x/12x^2-34=0
We multiply all the terms by the denominator
8x+9x-34*12x^2=0
We add all the numbers together, and all the variables
17x-34*12x^2=0
Wy multiply elements
-408x^2+17x=0
a = -408; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-408)·0
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-408}=\frac{-34}{-816} =1/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-408}=\frac{0}{-816} =0 $
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