x^2+32x+26=1

Solution for x^2+32x+26=1 equation:

x^2+32x+26=1

We move all terms to the left:

x^2+32x+26-(1)=0

We add all the numbers together, and all the variables

x^2+32x+25=0

a = 1; b = 32; c = +25;
Δ = b2-4ac
Δ = 322-4·1·25
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{231}}{2*1}=\frac{-32-2\sqrt{231}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{231}}{2*1}=\frac{-32+2\sqrt{231}}{2}
$