50=2x^2-5

Solution for 50=2x^2-5 equation:

50=2x^2-5

We move all terms to the left:

50-(2x^2-5)=0

We get rid of parentheses

-2x^2+5+50=0

We add all the numbers together, and all the variables

-2x^2+55=0

a = -2; b = 0; c = +55;
Δ = b2-4ac
Δ = 02-4·(-2)·55
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*-2}=\frac{0-2\sqrt{110}}{-4}
=-\frac{2\sqrt{110}}{-4}
=-\frac{\sqrt{110}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*-2}=\frac{0+2\sqrt{110}}{-4}
=\frac{2\sqrt{110}}{-4}
=\frac{\sqrt{110}}{-2}
$