15-1/5r=2r-1

Solution for 15-1/5r=2r-1 equation:

15-1/5r=2r-1

We move all terms to the left:

15-1/5r-(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+15=0

We multiply all the terms by the denominator


-2r*5r+1*5r+15*5r-1=0

Wy multiply elements

-10r^2+5r+75r-1=0

We add all the numbers together, and all the variables

-10r^2+80r-1=0

a = -10; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·(-10)·(-1)
Δ = 6360
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:

$\sqrt{\Delta}=\sqrt{6360}=\sqrt{4*1590}=\sqrt{4}*\sqrt{1590}=2\sqrt{1590}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1590}}{2*-10}=\frac{-80-2\sqrt{1590}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1590}}{2*-10}=\frac{-80+2\sqrt{1590}}{-20}
$