r-1/2r=1650

Solution for r-1/2r=1650 equation:

r-1/2r=1650

We move all terms to the left:

r-1/2r-(1650)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We multiply all the terms by the denominator


r*2r-1650*2r-1=0

Wy multiply elements

2r^2-3300r-1=0

a = 2; b = -3300; c = -1;
Δ = b2-4ac
Δ = -33002-4·2·(-1)
Δ = 10890008
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:

$\sqrt{\Delta}=\sqrt{10890008}=\sqrt{4*2722502}=\sqrt{4}*\sqrt{2722502}=2\sqrt{2722502}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3300)-2\sqrt{2722502}}{2*2}=\frac{3300-2\sqrt{2722502}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3300)+2\sqrt{2722502}}{2*2}=\frac{3300+2\sqrt{2722502}}{4}
$