How can I solve a quadratic equations for x in terms of y?

A quadratic involving x and y is usually in the form 'y = ax2 + bx + c'. This form is y in terms of x, so we must rearrange it.

y = ax2 + bx + c

y/a = x2 + bx/a + c/a

y/a = x2 + bx/a + d + e, where c/a = d + e, e = (b/a)2

y/a - e = x2 + bx/a + d

y/a -e = (x + b/a)2

√(y/a - e) = x + b/a

√(y/a - e) - b/a = x