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3/4x+19/6x=47/16
We move all terms to the left:
3/4x+19/6x-(47/16)=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!=0/6
x!=0
x∈R
3/4x+19/6x-(+47/16)=0
We get rid of parentheses
3/4x+19/6x-47/16=0
We calculate fractions
(-6768x^2)/384x^2+288x/384x^2+1216x/384x^2=0
We multiply all the terms by the denominator
(-6768x^2)+288x+1216x=0
We add all the numbers together, and all the variables
(-6768x^2)+1504x=0
We get rid of parentheses
-6768x^2+1504x=0
a = -6768; b = 1504; c = 0;
Δ = b2-4ac
Δ = 15042-4·(-6768)·0
Δ = 2262016
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{2262016}=1504$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1504)-1504}{2*-6768}=\frac{-3008}{-13536} =2/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1504)+1504}{2*-6768}=\frac{0}{-13536} =0 $
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