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3/8x+1/6x+5/12=69
We move all terms to the left:
3/8x+1/6x+5/12-(69)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 6x!=0determiningTheFunctionDomain 3/8x+1/6x-69+5/12=0
x!=0/6
x!=0
x∈R
We calculate fractions
1440x^2/576x^2+216x/576x^2+96x/576x^2-69=0
We multiply all the terms by the denominator
1440x^2+216x+96x-69*576x^2=0
We add all the numbers together, and all the variables
1440x^2+312x-69*576x^2=0
Wy multiply elements
1440x^2-39744x^2+312x=0
We add all the numbers together, and all the variables
-38304x^2+312x=0
a = -38304; b = 312; c = 0;
Δ = b2-4ac
Δ = 3122-4·(-38304)·0
Δ = 97344
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{97344}=312$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(312)-312}{2*-38304}=\frac{-624}{-76608} =13/1596 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(312)+312}{2*-38304}=\frac{0}{-76608} =0 $
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