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

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

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

We move all terms to the left:

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


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R



Domain of the equation: 5r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -10; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·(-10)·(-2)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{55}}{2*-10}=\frac{-60-8\sqrt{55}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{55}}{2*-10}=\frac{-60+8\sqrt{55}}{-20}
$