x*2x=473

Solution for x*2x=473 equation:

x*2x=473

We move all terms to the left:

x*2x-(473)=0

Wy multiply elements

2x^2-473=0

a = 2; b = 0; c = -473;
Δ = b2-4ac
Δ = 02-4·2·(-473)
Δ = 3784
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:

$\sqrt{\Delta}=\sqrt{3784}=\sqrt{4*946}=\sqrt{4}*\sqrt{946}=2\sqrt{946}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{946}}{2*2}=\frac{0-2\sqrt{946}}{4}
=-\frac{2\sqrt{946}}{4}
=-\frac{\sqrt{946}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{946}}{2*2}=\frac{0+2\sqrt{946}}{4}
=\frac{2\sqrt{946}}{4}
=\frac{\sqrt{946}}{2}
$