5r^2-24r-144=0

Solution for 5r^2-24r-144=0 equation:

5r^2-24r-144=0

a = 5; b = -24; c = -144;
Δ = b2-4ac
Δ = -242-4·5·(-144)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{6}}{2*5}=\frac{24-24\sqrt{6}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{6}}{2*5}=\frac{24+24\sqrt{6}}{10}
$