What is the exact solutions of x2=5x+2

Move all terms to the left of equal with changed sign

x²-5x-2 = 0

Solve with x₁,₂ = (-b±√Δ) / 2a

Δ = b²-4ac

call a (1) x², b - 5 and c - 2

x1,2 = ( - (-5) ±√ (-5) ²-4*1 * (-2)) / 2*1

x1,2 = (5±√25+8) / 2

x1,2 = (5 ± √33) / 2

x1 = (5+√33) / 2

x2 = (5-√33) / 2