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5/x+14=6/4x+5
We move all terms to the left:
5/x+14-(6/4x+5)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 4x+5)!=0We get rid of parentheses
x∈R
5/x-6/4x-5+14=0
We calculate fractions
20x/4x^2+(-6x)/4x^2-5+14=0
We add all the numbers together, and all the variables
20x/4x^2+(-6x)/4x^2+9=0
We multiply all the terms by the denominator
20x+(-6x)+9*4x^2=0
Wy multiply elements
36x^2+20x+(-6x)=0
We get rid of parentheses
36x^2+20x-6x=0
We add all the numbers together, and all the variables
36x^2+14x=0
a = 36; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·36·0
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*36}=\frac{-28}{72} =-7/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*36}=\frac{0}{72} =0 $
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