X2-8x=242

Solution for X2-8x=242 equation:

X2-8X=242

We move all terms to the left:

X2-8X-(242)=0

We add all the numbers together, and all the variables

X^2-8X-242=0

a = 1; b = -8; c = -242;
Δ = b2-4ac
Δ = -82-4·1·(-242)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{258}}{2*1}=\frac{8-2\sqrt{258}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{258}}{2*1}=\frac{8+2\sqrt{258}}{2}
$