12-5/1r=2r+1

Solution for 12-5/1r=2r+1 equation:

12-5/1r=2r+1

We move all terms to the left:

12-5/1r-(2r+1)=0


Domain of the equation: 1r!=0

r∈R


We get rid of parentheses

-5/1r-2r-1+12=0

We multiply all the terms by the denominator


-2r*1r-1*1r+12*1r-5=0

Wy multiply elements

-2r^2-1r+12r-5=0

We add all the numbers together, and all the variables

-2r^2+11r-5=0

a = -2; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-2)·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-2}=\frac{-20}{-4}
=+5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-2}=\frac{-2}{-4}
=1/2
$