x^2+32x=13

Solution for x^2+32x=13 equation:

x^2+32x=13

We move all terms to the left:

x^2+32x-(13)=0

a = 1; b = 32; c = -13;
Δ = b2-4ac
Δ = 322-4·1·(-13)
Δ = 1076
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:

$\sqrt{\Delta}=\sqrt{1076}=\sqrt{4*269}=\sqrt{4}*\sqrt{269}=2\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{269}}{2*1}=\frac{-32-2\sqrt{269}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{269}}{2*1}=\frac{-32+2\sqrt{269}}{2}
$