26=12x-x^2

Solution for 26=12x-x^2 equation:

26=12x-x^2

We move all terms to the left:

26-(12x-x^2)=0

We get rid of parentheses

x^2-12x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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