5r^2+9r=-1

Solution for 5r^2+9r=-1 equation:

5r^2+9r=-1

We move all terms to the left:

5r^2+9r-(-1)=0

We add all the numbers together, and all the variables

5r^2+9r+1=0

a = 5; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·5·1
Δ = 61
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{61}}{2*5}=\frac{-9-\sqrt{61}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{61}}{2*5}=\frac{-9+\sqrt{61}}{10}
$