25x^2-14x-31=0

Solution for 25x^2-14x-31=0 equation:

25x^2-14x-31=0

a = 25; b = -14; c = -31;
Δ = b2-4ac
Δ = -142-4·25·(-31)
Δ = 3296
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:

$\sqrt{\Delta}=\sqrt{3296}=\sqrt{16*206}=\sqrt{16}*\sqrt{206}=4\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{206}}{2*25}=\frac{14-4\sqrt{206}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{206}}{2*25}=\frac{14+4\sqrt{206}}{50}
$