r2-9r-38=-9

Solution for r2-9r-38=-9 equation:

r2-9r-38=-9

We move all terms to the left:

r2-9r-38-(-9)=0

We add all the numbers together, and all the variables

r^2-9r-29=0

a = 1; b = -9; c = -29;
Δ = b2-4ac
Δ = -92-4·1·(-29)
Δ = 197
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{197}}{2*1}=\frac{9-\sqrt{197}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{197}}{2*1}=\frac{9+\sqrt{197}}{2}
$