r2+9r=19

Solution for r2+9r=19 equation:

r2+9r=19

We move all terms to the left:

r2+9r-(19)=0

We add all the numbers together, and all the variables

r^2+9r-19=0

a = 1; b = 9; c = -19;
Δ = b2-4ac
Δ = 92-4·1·(-19)
Δ = 157
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{157}}{2*1}=\frac{-9-\sqrt{157}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{157}}{2*1}=\frac{-9+\sqrt{157}}{2}
$