With the information you entered here, you can't find a specific answer for x and y. Whenever you have two variables in an equation, there are an infinite number of possible solutions. When neither variable has a written exponent (meaning the exponent is 1), then all of the possible solutions actually form a straight line on a coordinate plane. In this example, with x raised to the second power, the possible solutions form a parabola when graphed.
We can simplify this equation and get it into the form of a quadratic equation (y = ax^2 + bx +c) by combining like terms:
20x + x^2 - 8 + 5y = 0
Then move the y term to the other side:
20x + x^2 - 8 = -5y
You then divide both sides by -5. That's a little difficult to express by typing, so I'll leave that for you to do on paper. I divided each term by -5 and rearranged them to match the quadratic form:
y = - 1/5 x^2 - 4x + 8/5
From here, you really need more information, like another equation, to solve for x and y, because there are an infinite number of solutions. (You could pick any number for x and substitute it in the equation to find y.)
If there is a second equation, I could show you how to solve the "system of equations." There would be only one pair of numbers that would fit both equations.