12+1/5r=2r+1

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

12+1/5r=2r+1

We move all terms to the left:

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


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10r^2-5r+60r+1=0

We add all the numbers together, and all the variables

-10r^2+55r+1=0

a = -10; b = 55; c = +1;
Δ = b2-4ac
Δ = 552-4·(-10)·1
Δ = 3065
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{-(55)-\sqrt{3065}}{2*-10}=\frac{-55-\sqrt{3065}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3065}}{2*-10}=\frac{-55+\sqrt{3065}}{-20}
$