9r^2-12r-59=0

Solution for 9r^2-12r-59=0 equation:

9r^2-12r-59=0

a = 9; b = -12; c = -59;
Δ = b2-4ac
Δ = -122-4·9·(-59)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18\sqrt{7}}{2*9}=\frac{12-18\sqrt{7}}{18}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18\sqrt{7}}{2*9}=\frac{12+18\sqrt{7}}{18}
$