2x*x=428

Solution for 2x*x=428 equation:

2x*x=428

We move all terms to the left:

2x*x-(428)=0

Wy multiply elements

2x^2-428=0

a = 2; b = 0; c = -428;
Δ = b2-4ac
Δ = 02-4·2·(-428)
Δ = 3424
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:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{214}}{2*2}=\frac{0-4\sqrt{214}}{4}
=-\frac{4\sqrt{214}}{4}
=-\sqrt{214}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{214}}{2*2}=\frac{0+4\sqrt{214}}{4}
=\frac{4\sqrt{214}}{4}
=\sqrt{214}
$