0.5r-3=12-9/2r

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Solution for 0.5r-3=12-9/2r equation:



0.5r-3=12-9/2r
We move all terms to the left:
0.5r-3-(12-9/2r)=0
Domain of the equation: 2r)!=0
r!=0/1
r!=0
r∈R
We add all the numbers together, and all the variables
0.5r-(-9/2r+12)-3=0
We get rid of parentheses
0.5r+9/2r-12-3=0
We multiply all the terms by the denominator
(0.5r)*2r-12*2r-3*2r+9=0
We add all the numbers together, and all the variables
(+0.5r)*2r-12*2r-3*2r+9=0
We multiply parentheses
0r^2-12*2r-3*2r+9=0
Wy multiply elements
0r^2-24r-6r+9=0
We add all the numbers together, and all the variables
r^2-30r+9=0
a = 1; b = -30; c = +9;
Δ = b2-4ac
Δ = -302-4·1·9
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12\sqrt{6}}{2*1}=\frac{30-12\sqrt{6}}{2} $
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{6}}{2*1}=\frac{30+12\sqrt{6}}{2} $

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