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7/5x+25-3/x+5=2/5
We move all terms to the left:
7/5x+25-3/x+5-(2/5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
7/5x-3/x+25+5-(+2/5)=0
We add all the numbers together, and all the variables
7/5x-3/x+30-(+2/5)=0
We get rid of parentheses
7/5x-3/x+30-2/5=0
We calculate fractions
7x/125x^2+(-375x)/125x^2+(-2x)/125x^2+30=0
We multiply all the terms by the denominator
7x+(-375x)+(-2x)+30*125x^2=0
Wy multiply elements
3750x^2+7x+(-375x)+(-2x)=0
We get rid of parentheses
3750x^2+7x-375x-2x=0
We add all the numbers together, and all the variables
3750x^2-370x=0
a = 3750; b = -370; c = 0;
Δ = b2-4ac
Δ = -3702-4·3750·0
Δ = 136900
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{136900}=370$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-370)-370}{2*3750}=\frac{0}{7500} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-370)+370}{2*3750}=\frac{740}{7500} =37/375 $
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