3/5r-3=5/r

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Solution for 3/5r-3=5/r equation:



3/5r-3=5/r
We move all terms to the left:
3/5r-3-(5/r)=0
Domain of the equation: 5r!=0
r!=0/5
r!=0
r∈R
Domain of the equation: r)!=0
r!=0/1
r!=0
r∈R
We add all the numbers together, and all the variables
3/5r-(+5/r)-3=0
We get rid of parentheses
3/5r-5/r-3=0
We calculate fractions
3r/5r^2+(-25r)/5r^2-3=0
We multiply all the terms by the denominator
3r+(-25r)-3*5r^2=0
Wy multiply elements
-15r^2+3r+(-25r)=0
We get rid of parentheses
-15r^2+3r-25r=0
We add all the numbers together, and all the variables
-15r^2-22r=0
a = -15; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-15)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-15}=\frac{0}{-30} =0 $
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-15}=\frac{44}{-30} =-1+7/15 $

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