x(x-4)+x=26

Solution for x(x-4)+x=26 equation:

x(x-4)+x=26

We move all terms to the left:

x(x-4)+x-(26)=0

We add all the numbers together, and all the variables

x+x(x-4)-26=0

We multiply parentheses

x^2+x-4x-26=0

We add all the numbers together, and all the variables

x^2-3x-26=0

a = 1; b = -3; c = -26;
Δ = b2-4ac
Δ = -32-4·1·(-26)
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{113}}{2*1}=\frac{3-\sqrt{113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{113}}{2*1}=\frac{3+\sqrt{113}}{2}
$