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1/4x+2/3x+7=84
We move all terms to the left:
1/4x+2/3x+7-(84)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1/4x+2/3x-77=0
We calculate fractions
3x/12x^2+8x/12x^2-77=0
We multiply all the terms by the denominator
3x+8x-77*12x^2=0
We add all the numbers together, and all the variables
11x-77*12x^2=0
Wy multiply elements
-924x^2+11x=0
a = -924; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-924)·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-924}=\frac{-22}{-1848} =1/84 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-924}=\frac{0}{-1848} =0 $
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