25x^2-72x-144=0

Solution for 25x^2-72x-144=0 equation:

25x^2-72x-144=0

a = 25; b = -72; c = -144;
Δ = b2-4ac
Δ = -722-4·25·(-144)
Δ = 19584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{34}}{2*25}=\frac{72-24\sqrt{34}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{34}}{2*25}=\frac{72+24\sqrt{34}}{50}
$