r=1/660r-4

Solution for r=1/660r-4 equation:

r=1/660r-4

We move all terms to the left:

r-(1/660r-4)=0


Domain of the equation: 660r-4)!=0

r∈R


We get rid of parentheses

r-1/660r+4=0

We multiply all the terms by the denominator


r*660r+4*660r-1=0

Wy multiply elements

660r^2+2640r-1=0

a = 660; b = 2640; c = -1;
Δ = b2-4ac
Δ = 26402-4·660·(-1)
Δ = 6972240
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:

$\sqrt{\Delta}=\sqrt{6972240}=\sqrt{16*435765}=\sqrt{16}*\sqrt{435765}=4\sqrt{435765}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2640)-4\sqrt{435765}}{2*660}=\frac{-2640-4\sqrt{435765}}{1320}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2640)+4\sqrt{435765}}{2*660}=\frac{-2640+4\sqrt{435765}}{1320}
$