5x^2-2x-25=0

Solution for 5x^2-2x-25=0 equation:

5x^2-2x-25=0

a = 5; b = -2; c = -25;
Δ = b2-4ac
Δ = -22-4·5·(-25)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{14}}{2*5}=\frac{2-6\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{14}}{2*5}=\frac{2+6\sqrt{14}}{10}
$