x^2-18x-62=6

Solution for x^2-18x-62=6 equation:

x^2-18x-62=6

We move all terms to the left:

x^2-18x-62-(6)=0

We add all the numbers together, and all the variables

x^2-18x-68=0

a = 1; b = -18; c = -68;
Δ = b2-4ac
Δ = -182-4·1·(-68)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{149}}{2*1}=\frac{18-2\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{149}}{2*1}=\frac{18+2\sqrt{149}}{2}
$