r=1/6.60r-4

Solution for r=1/6.60r-4 equation:

r=1/6.60r-4

We move all terms to the left:

r-(1/6.60r-4)=0


Domain of the equation: 6.60r-4)!=0

r∈R


We get rid of parentheses

r-1/6.60r+4=0

We multiply all the terms by the denominator


r*6.60r+4*6.60r-1=0

Wy multiply elements

6r^2+24r-1=0

a = 6; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·6·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*6}=\frac{-24-10\sqrt{6}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*6}=\frac{-24+10\sqrt{6}}{12}
$