4.29=r^2+2r

Solution for 4.29=r^2+2r equation:

4.29=r^2+2r

We move all terms to the left:

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

We get rid of parentheses

-r^2-2r+4.29=0

We add all the numbers together, and all the variables

-1r^2-2r+4.29=0

a = -1; b = -2; c = +4.29;
Δ = b2-4ac
Δ = -22-4·(-1)·4.29
Δ = 21.16
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{-(-2)-\sqrt{21.16}}{2*-1}=\frac{2-\sqrt{21.16}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{21.16}}{2*-1}=\frac{2+\sqrt{21.16}}{-2}
$