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+65r-1=0

a = -10; b = 65; c = -1;
Δ = b2-4ac
Δ = 652-4·(-10)·(-1)
Δ = 4185
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:

$\sqrt{\Delta}=\sqrt{4185}=\sqrt{9*465}=\sqrt{9}*\sqrt{465}=3\sqrt{465}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-3\sqrt{465}}{2*-10}=\frac{-65-3\sqrt{465}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+3\sqrt{465}}{2*-10}=\frac{-65+3\sqrt{465}}{-20}
$