1/2r-3=12-9/6r

Solution for 1/2r-3=12-9/6r equation:

1/2r-3=12-9/6r

We move all terms to the left:

1/2r-3-(12-9/6r)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 6r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

1/2r-(-9/6r+12)-3=0

We get rid of parentheses

1/2r+9/6r-12-3=0

We calculate fractions


6r/12r^2+18r/12r^2-12-3=0

We add all the numbers together, and all the variables

6r/12r^2+18r/12r^2-15=0

We multiply all the terms by the denominator


6r+18r-15*12r^2=0

We add all the numbers together, and all the variables

24r-15*12r^2=0

Wy multiply elements

-180r^2+24r=0

a = -180; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-180)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-180}=\frac{-48}{-360}
=2/15
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-180}=\frac{0}{-360}
=0
$