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11/2x+11/4x=22
We move all terms to the left:
11/2x+11/4x-(22)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x!=0We calculate fractions
x!=0/4
x!=0
x∈R
44x/8x^2+22x/8x^2-22=0
We multiply all the terms by the denominator
44x+22x-22*8x^2=0
We add all the numbers together, and all the variables
66x-22*8x^2=0
Wy multiply elements
-176x^2+66x=0
a = -176; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-176)·0
Δ = 4356
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{4356}=66$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-176}=\frac{-132}{-352} =3/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-176}=\frac{0}{-352} =0 $
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