x^2-6x-4=32

Solution for x^2-6x-4=32 equation:

x^2-6x-4=32

We move all terms to the left:

x^2-6x-4-(32)=0

We add all the numbers together, and all the variables

x^2-6x-36=0

a = 1; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·1·(-36)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*1}=\frac{6-6\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*1}=\frac{6+6\sqrt{5}}{2}
$