2r-1/5r=11

Solution for 2r-1/5r=11 equation:

2r-1/5r=11

We move all terms to the left:

2r-1/5r-(11)=0


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R


We multiply all the terms by the denominator


2r*5r-11*5r-1=0

Wy multiply elements

10r^2-55r-1=0

a = 10; b = -55; c = -1;
Δ = b2-4ac
Δ = -552-4·10·(-1)
Δ = 3065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{3065}}{2*10}=\frac{55-\sqrt{3065}}{20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3065}}{2*10}=\frac{55+\sqrt{3065}}{20}
$