x2+32x=1

Solution for x2+32x=1 equation:

x2+32x=1

We move all terms to the left:

x2+32x-(1)=0

We add all the numbers together, and all the variables

x^2+32x-1=0

a = 1; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·1·(-1)
Δ = 1028
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:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{257}}{2*1}=\frac{-32-2\sqrt{257}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{257}}{2*1}=\frac{-32+2\sqrt{257}}{2}
$