3-1/2r=6-2/3r

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Solution for 3-1/2r=6-2/3r equation:



3-1/2r=6-2/3r
We move all terms to the left:
3-1/2r-(6-2/3r)=0
Domain of the equation: 2r!=0
r!=0/2
r!=0
r∈R
Domain of the equation: 3r)!=0
r!=0/1
r!=0
r∈R
We add all the numbers together, and all the variables
-1/2r-(-2/3r+6)+3=0
We get rid of parentheses
-1/2r+2/3r-6+3=0
We calculate fractions
(-3r)/6r^2+4r/6r^2-6+3=0
We add all the numbers together, and all the variables
(-3r)/6r^2+4r/6r^2-3=0
We multiply all the terms by the denominator
(-3r)+4r-3*6r^2=0
We add all the numbers together, and all the variables
4r+(-3r)-3*6r^2=0
Wy multiply elements
-18r^2+4r+(-3r)=0
We get rid of parentheses
-18r^2+4r-3r=0
We add all the numbers together, and all the variables
-18r^2+r=0
a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-18}=\frac{-2}{-36} =1/18 $
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-18}=\frac{0}{-36} =0 $

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