16.5+3/2r=12+2r

Solution for 16.5+3/2r=12+2r equation:

16.5+3/2r=12+2r

We move all terms to the left:

16.5+3/2r-(12+2r)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

3/2r-(2r+12)+16.5=0

We get rid of parentheses

3/2r-2r-12+16.5=0

We multiply all the terms by the denominator


-2r*2r-12*2r+(16.5)*2r+3=0

We multiply parentheses

-2r*2r-12*2r+33r+3=0

Wy multiply elements

-4r^2-24r+33r+3=0

We add all the numbers together, and all the variables

-4r^2+9r+3=0

a = -4; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-4)·3
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{129}}{2*-4}=\frac{-9-\sqrt{129}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*-4}=\frac{-9+\sqrt{129}}{-8}
$