49=2x^2

Solution for 49=2x^2 equation:

49=2x^2

We move all terms to the left:

49-(2x^2)=0

a = -2; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-2)·49
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*-2}=\frac{0-14\sqrt{2}}{-4}
=-\frac{14\sqrt{2}}{-4}
=-\frac{7\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*-2}=\frac{0+14\sqrt{2}}{-4}
=\frac{14\sqrt{2}}{-4}
=\frac{7\sqrt{2}}{-2}
$