[tex]-x^2+5x-6=2\\-x^2+5x-6-2=0\\-x^2+5x-8=0\\[/tex]
↝ Form into [tex]ax^2+bx+c = 0[/tex] where a > 0 (Optional)
[tex]x^2-5x+8=0[/tex] ↝ Multiply -1 for both sides.
↝ Then proceed with the Quadratic Formula.
x = [-b ± (√b²-4ac)]/2a ↝ Quadratic Formula
[tex]x=\frac{-(-5)+-\sqrt{(-5)^2-4(1)(8)}}{2(1)}\\x=\frac{5+-\sqrt{25-32}}{2}\\[/tex]
↝ As you can see that inside the square root, the numbers cannot be negative. Therefore, the solutions are imaginary.
↝ Solution with Real Numbers System ↝ There are no real solutions.
↝ Solution with Complex Number System ↝
[tex]x=\frac{5+-\sqrt{25-32}}{2}\\x=\frac{5+-\sqrt{-7}}{2}\\x=\frac{5+-\sqrt{7}i }{2}[/tex]
Therefore, the answer for Complex Number System is (5±√7i)/2
