2x^2=4900

Solution for 2x^2=4900 equation:

2x^2=4900

We move all terms to the left:

2x^2-(4900)=0

a = 2; b = 0; c = -4900;
Δ = b2-4ac
Δ = 02-4·2·(-4900)
Δ = 39200
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:

$\sqrt{\Delta}=\sqrt{39200}=\sqrt{19600*2}=\sqrt{19600}*\sqrt{2}=140\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140\sqrt{2}}{2*2}=\frac{0-140\sqrt{2}}{4}
=-\frac{140\sqrt{2}}{4}
=-35\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140\sqrt{2}}{2*2}=\frac{0+140\sqrt{2}}{4}
=\frac{140\sqrt{2}}{4}
=35\sqrt{2}
$