2x(x-13)=26

Solution for 2x(x-13)=26 equation:

2x(x-13)=26

We move all terms to the left:

2x(x-13)-(26)=0

We multiply parentheses

2x^2-26x-26=0

a = 2; b = -26; c = -26;
Δ = b2-4ac
Δ = -262-4·2·(-26)
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{221}}{2*2}=\frac{26-2\sqrt{221}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{221}}{2*2}=\frac{26+2\sqrt{221}}{4}
$