Omar Khayyam’s cubic equation type?

This is Omar Khayyam’s cubic equation type: A cube plus squares plus sides equals a number. Represent this as the equation x3 + bx2 + cx = d. This class of cubics is solved by the intersection of a circle and a hyperbola. Determine the equations of the two conic sections in terms of the given coefficients in the cubic equation. Show algebraically that their intersection does in fact give a solution to the cubic. Then translate Omar Khayyam’s proof of his construction into modern terms and compare with the algebraic solution.