X(x*4)=242

Solution for X(x*4)=242 equation:

X(X*4)=242

We move all terms to the left:

X(X*4)-(242)=0

We add all the numbers together, and all the variables

X(+X*4)-242=0

We multiply parentheses

4X^2-242=0

a = 4; b = 0; c = -242;
Δ = b2-4ac
Δ = 02-4·4·(-242)
Δ = 3872
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:

$\sqrt{\Delta}=\sqrt{3872}=\sqrt{1936*2}=\sqrt{1936}*\sqrt{2}=44\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-44\sqrt{2}}{2*4}=\frac{0-44\sqrt{2}}{8}
=-\frac{44\sqrt{2}}{8}
=-\frac{11\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+44\sqrt{2}}{2*4}=\frac{0+44\sqrt{2}}{8}
=\frac{44\sqrt{2}}{8}
=\frac{11\sqrt{2}}{2}
$