r2=3(r+1)

Solution for r2=3(r+1) equation:

r2=3(r+1)

We move all terms to the left:

r2-(3(r+1))=0

We add all the numbers together, and all the variables

r^2-(3(r+1))=0


We calculate terms in parentheses: -(3(r+1)), so:

3(r+1)

We multiply parentheses

3r+3

Back to the equation:

-(3r+3)


We get rid of parentheses

r^2-3r-3=0

a = 1; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·1·(-3)
Δ = 21
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{-(-3)-\sqrt{21}}{2*1}=\frac{3-\sqrt{21}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*1}=\frac{3+\sqrt{21}}{2}
$