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8/5+3/x=7/4x
We move all terms to the left:
8/5+3/x-(7/4x)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/x-(+7/4x)+8/5=0
We get rid of parentheses
3/x-7/4x+8/5=0
We calculate fractions
128x^2/100x^2+300x/100x^2+(-175x)/100x^2=0
We multiply all the terms by the denominator
128x^2+300x+(-175x)=0
We get rid of parentheses
128x^2+300x-175x=0
We add all the numbers together, and all the variables
128x^2+125x=0
a = 128; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·128·0
Δ = 15625
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{15625}=125$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*128}=\frac{-250}{256} =-125/128 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*128}=\frac{0}{256} =0 $
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