50=2x^2+3

Solution for 50=2x^2+3 equation:

50=2x^2+3

We move all terms to the left:

50-(2x^2+3)=0

We get rid of parentheses

-2x^2-3+50=0

We add all the numbers together, and all the variables

-2x^2+47=0

a = -2; b = 0; c = +47;
Δ = b2-4ac
Δ = 02-4·(-2)·47
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{94}}{2*-2}=\frac{0-2\sqrt{94}}{-4}
=-\frac{2\sqrt{94}}{-4}
=-\frac{\sqrt{94}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{94}}{2*-2}=\frac{0+2\sqrt{94}}{-4}
=\frac{2\sqrt{94}}{-4}
=\frac{\sqrt{94}}{-2}
$