25X^2-4x-19=0

Solution for 25X^2-4x-19=0 equation:

25X^2-4X-19=0

a = 25; b = -4; c = -19;
Δ = b2-4ac
Δ = -42-4·25·(-19)
Δ = 1916
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:

$\sqrt{\Delta}=\sqrt{1916}=\sqrt{4*479}=\sqrt{4}*\sqrt{479}=2\sqrt{479}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{479}}{2*25}=\frac{4-2\sqrt{479}}{50}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{479}}{2*25}=\frac{4+2\sqrt{479}}{50}
$