1725=r+1/2r

Solution for 1725=r+1/2r equation:

1725=r+1/2r

We move all terms to the left:

1725-(r+1/2r)=0


Domain of the equation: 2r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

-(+r+1/2r)+1725=0

We get rid of parentheses

-r-1/2r+1725=0

We multiply all the terms by the denominator


-r*2r+1725*2r-1=0

Wy multiply elements

-2r^2+3450r-1=0

a = -2; b = 3450; c = -1;
Δ = b2-4ac
Δ = 34502-4·(-2)·(-1)
Δ = 11902492
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:

$\sqrt{\Delta}=\sqrt{11902492}=\sqrt{196*60727}=\sqrt{196}*\sqrt{60727}=14\sqrt{60727}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3450)-14\sqrt{60727}}{2*-2}=\frac{-3450-14\sqrt{60727}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3450)+14\sqrt{60727}}{2*-2}=\frac{-3450+14\sqrt{60727}}{-4}
$