24x^2-6x-25=0

Solution for 24x^2-6x-25=0 equation:

24x^2-6x-25=0

a = 24; b = -6; c = -25;
Δ = b2-4ac
Δ = -62-4·24·(-25)
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{609}}{2*24}=\frac{6-2\sqrt{609}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{609}}{2*24}=\frac{6+2\sqrt{609}}{48}
$