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14/2x+4=27/5x+2
We move all terms to the left:
14/2x+4-(27/5x+2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x+2)!=0We get rid of parentheses
x∈R
14/2x-27/5x-2+4=0
We calculate fractions
70x/10x^2+(-54x)/10x^2-2+4=0
We add all the numbers together, and all the variables
70x/10x^2+(-54x)/10x^2+2=0
We multiply all the terms by the denominator
70x+(-54x)+2*10x^2=0
Wy multiply elements
20x^2+70x+(-54x)=0
We get rid of parentheses
20x^2+70x-54x=0
We add all the numbers together, and all the variables
20x^2+16x=0
a = 20; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·20·0
Δ = 256
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{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*20}=\frac{-32}{40} =-4/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*20}=\frac{0}{40} =0 $
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