12-1/2r=2r+1

Solution for 12-1/2r=2r+1 equation:

12-1/2r=2r+1

We move all terms to the left:

12-1/2r-(2r+1)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We get rid of parentheses

-1/2r-2r-1+12=0

We multiply all the terms by the denominator


-2r*2r-1*2r+12*2r-1=0

Wy multiply elements

-4r^2-2r+24r-1=0

We add all the numbers together, and all the variables

-4r^2+22r-1=0

a = -4; b = 22; c = -1;
Δ = b2-4ac
Δ = 222-4·(-4)·(-1)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{13}}{2*-4}=\frac{-22-6\sqrt{13}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{13}}{2*-4}=\frac{-22+6\sqrt{13}}{-8}
$