9r^2-39r-9=0

Solution for 9r^2-39r-9=0 equation:

9r^2-39r-9=0

a = 9; b = -39; c = -9;
Δ = b2-4ac
Δ = -392-4·9·(-9)
Δ = 1845
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1845}=\sqrt{9*205}=\sqrt{9}*\sqrt{205}=3\sqrt{205}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{205}}{2*9}=\frac{39-3\sqrt{205}}{18}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{205}}{2*9}=\frac{39+3\sqrt{205}}{18}
$