1/5r-12=2r+1

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

1/5r-12=2r+1

We move all terms to the left:

1/5r-12-(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^2-65r+1=0

a = -10; b = -65; c = +1;
Δ = b2-4ac
Δ = -652-4·(-10)·1
Δ = 4265
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{-(-65)-\sqrt{4265}}{2*-10}=\frac{65-\sqrt{4265}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4265}}{2*-10}=\frac{65+\sqrt{4265}}{-20}
$