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11/x=-3/4x-4
We move all terms to the left:
11/x-(-3/4x-4)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 4x-4)!=0We get rid of parentheses
x∈R
11/x+3/4x+4=0
We calculate fractions
44x/4x^2+3x/4x^2+4=0
We multiply all the terms by the denominator
44x+3x+4*4x^2=0
We add all the numbers together, and all the variables
47x+4*4x^2=0
Wy multiply elements
16x^2+47x=0
a = 16; b = 47; c = 0;
Δ = b2-4ac
Δ = 472-4·16·0
Δ = 2209
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{2209}=47$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-47}{2*16}=\frac{-94}{32} =-2+15/16 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+47}{2*16}=\frac{0}{32} =0 $
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