x2-25x+19=0

Solution for x2-25x+19=0 equation:

x2-25x+19=0

We add all the numbers together, and all the variables

x^2-25x+19=0

a = 1; b = -25; c = +19;
Δ = b2-4ac
Δ = -252-4·1·19
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{61}}{2*1}=\frac{25-3\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{61}}{2*1}=\frac{25+3\sqrt{61}}{2}
$