x2-26x+14=0

Solution for x2-26x+14=0 equation:

x2-26x+14=0

We add all the numbers together, and all the variables

x^2-26x+14=0

a = 1; b = -26; c = +14;
Δ = b2-4ac
Δ = -262-4·1·14
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{155}}{2*1}=\frac{26-2\sqrt{155}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{155}}{2*1}=\frac{26+2\sqrt{155}}{2}
$