x2+26x=23

Solution for x2+26x=23 equation:

x2+26x=23

We move all terms to the left:

x2+26x-(23)=0

We add all the numbers together, and all the variables

x^2+26x-23=0

a = 1; b = 26; c = -23;
Δ = b2-4ac
Δ = 262-4·1·(-23)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-16\sqrt{3}}{2*1}=\frac{-26-16\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+16\sqrt{3}}{2*1}=\frac{-26+16\sqrt{3}}{2}
$