a2-12a+26=0

Solution for a2-12a+26=0 equation:

a2-12a+26=0

We add all the numbers together, and all the variables

a^2-12a+26=0

a = 1; b = -12; c = +26;
Δ = b2-4ac
Δ = -122-4·1·26
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{10}}{2*1}=\frac{12-2\sqrt{10}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{10}}{2*1}=\frac{12+2\sqrt{10}}{2}
$