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3/x+4=5/5x+1
We move all terms to the left:
3/x+4-(5/5x+1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 5x+1)!=0We get rid of parentheses
x∈R
3/x-5/5x-1+4=0
We calculate fractions
15x/5x^2+(-5x)/5x^2-1+4=0
We add all the numbers together, and all the variables
15x/5x^2+(-5x)/5x^2+3=0
We multiply all the terms by the denominator
15x+(-5x)+3*5x^2=0
Wy multiply elements
15x^2+15x+(-5x)=0
We get rid of parentheses
15x^2+15x-5x=0
We add all the numbers together, and all the variables
15x^2+10x=0
a = 15; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·15·0
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*15}=\frac{-20}{30} =-2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*15}=\frac{0}{30} =0 $
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