(2/r-1)-(4r+1)=7

Solution for (2/r-1)-(4r+1)=7 equation:

(2/r-1)-(4r+1)=7

We move all terms to the left:

(2/r-1)-(4r+1)-(7)=0


Domain of the equation: r-1)!=0

r∈R


We get rid of parentheses

2/r-4r-1-1-7=0

We multiply all the terms by the denominator


-4r*r-1*r-1*r-7*r+2=0

We add all the numbers together, and all the variables

-9r-4r*r+2=0

Wy multiply elements

-4r^2-9r+2=0

a = -4; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-4)·2
Δ = 113
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{-(-9)-\sqrt{113}}{2*-4}=\frac{9-\sqrt{113}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{113}}{2*-4}=\frac{9+\sqrt{113}}{-8}
$