x*2x-2=420

Solution for x*2x-2=420 equation:

x*2x-2=420

We move all terms to the left:

x*2x-2-(420)=0

We add all the numbers together, and all the variables

x*2x-422=0

Wy multiply elements

2x^2-422=0

a = 2; b = 0; c = -422;
Δ = b2-4ac
Δ = 02-4·2·(-422)
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{211}}{2*2}=\frac{0-4\sqrt{211}}{4}
=-\frac{4\sqrt{211}}{4}
=-\sqrt{211}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{211}}{2*2}=\frac{0+4\sqrt{211}}{4}
=\frac{4\sqrt{211}}{4}
=\sqrt{211}
$