25x^2-10x-256=0

Solution for 25x^2-10x-256=0 equation:

25x^2-10x-256=0

a = 25; b = -10; c = -256;
Δ = b2-4ac
Δ = -102-4·25·(-256)
Δ = 25700
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:

$\sqrt{\Delta}=\sqrt{25700}=\sqrt{100*257}=\sqrt{100}*\sqrt{257}=10\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{257}}{2*25}=\frac{10-10\sqrt{257}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{257}}{2*25}=\frac{10+10\sqrt{257}}{50}
$