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1/4x+1/5x=1100
We move all terms to the left:
1/4x+1/5x-(1100)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 5x!=0We calculate fractions
x!=0/5
x!=0
x∈R
5x/20x^2+4x/20x^2-1100=0
We multiply all the terms by the denominator
5x+4x-1100*20x^2=0
We add all the numbers together, and all the variables
9x-1100*20x^2=0
Wy multiply elements
-22000x^2+9x=0
a = -22000; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-22000)·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-22000}=\frac{-18}{-44000} =9/22000 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-22000}=\frac{0}{-44000} =0 $
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