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4/9x+1/4x=11
We move all terms to the left:
4/9x+1/4x-(11)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 4x!=0We calculate fractions
x!=0/4
x!=0
x∈R
16x/36x^2+9x/36x^2-11=0
We multiply all the terms by the denominator
16x+9x-11*36x^2=0
We add all the numbers together, and all the variables
25x-11*36x^2=0
Wy multiply elements
-396x^2+25x=0
a = -396; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-396)·0
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-396}=\frac{-50}{-792} =25/396 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-396}=\frac{0}{-792} =0 $
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