x^2-16x+52=-6

Solution for x^2-16x+52=-6 equation:

x^2-16x+52=-6

We move all terms to the left:

x^2-16x+52-(-6)=0

We add all the numbers together, and all the variables

x^2-16x+58=0

a = 1; b = -16; c = +58;
Δ = b2-4ac
Δ = -162-4·1·58
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{6}}{2*1}=\frac{16-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{6}}{2*1}=\frac{16+2\sqrt{6}}{2}
$