(r-1)(2r+1)=2

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

(r-1)(2r+1)=2

We move all terms to the left:

(r-1)(2r+1)-(2)=0

We multiply parentheses ..

(+2r^2+r-2r-1)-2=0

We get rid of parentheses

2r^2+r-2r-1-2=0

We add all the numbers together, and all the variables

2r^2-1r-3=0

a = 2; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·2·(-3)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*2}=\frac{-4}{4}
=-1
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*2}=\frac{6}{4}
=1+1/2
$