55=2x^2-5

Solution for 55=2x^2-5 equation:

55=2x^2-5

We move all terms to the left:

55-(2x^2-5)=0

We get rid of parentheses

-2x^2+5+55=0

We add all the numbers together, and all the variables

-2x^2+60=0

a = -2; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-2)·60
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-2}=\frac{0-4\sqrt{30}}{-4}
=-\frac{4\sqrt{30}}{-4}
=-\frac{\sqrt{30}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-2}=\frac{0+4\sqrt{30}}{-4}
=\frac{4\sqrt{30}}{-4}
=\frac{\sqrt{30}}{-1}
$