12-1/5r=2r+r

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

12-1/5r=2r+r

We move all terms to the left:

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


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R


We add all the numbers together, and all the variables

-1/5r-(+3r)+12=0

We get rid of parentheses

-1/5r-3r+12=0

We multiply all the terms by the denominator


-3r*5r+12*5r-1=0

Wy multiply elements

-15r^2+60r-1=0

a = -15; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·(-15)·(-1)
Δ = 3540
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:

$\sqrt{\Delta}=\sqrt{3540}=\sqrt{4*885}=\sqrt{4}*\sqrt{885}=2\sqrt{885}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{885}}{2*-15}=\frac{-60-2\sqrt{885}}{-30}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{885}}{2*-15}=\frac{-60+2\sqrt{885}}{-30}
$