25x^2-24x-13=0

Solution for 25x^2-24x-13=0 equation:

25x^2-24x-13=0

a = 25; b = -24; c = -13;
Δ = b2-4ac
Δ = -242-4·25·(-13)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{469}}{2*25}=\frac{24-2\sqrt{469}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{469}}{2*25}=\frac{24+2\sqrt{469}}{50}
$