x^2=6x+39

Solution for x^2=6x+39 equation:

x^2=6x+39

We move all terms to the left:

x^2-(6x+39)=0

We get rid of parentheses

x^2-6x-39=0

a = 1; b = -6; c = -39;
Δ = b2-4ac
Δ = -62-4·1·(-39)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{3}}{2*1}=\frac{6-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{3}}{2*1}=\frac{6+8\sqrt{3}}{2}
$