x^2-25x+5=0

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

x^2-25x+5=0

a = 1; b = -25; c = +5;
Δ = b2-4ac
Δ = -252-4·1·5
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11\sqrt{5}}{2*1}=\frac{25-11\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11\sqrt{5}}{2*1}=\frac{25+11\sqrt{5}}{2}
$