To solve a quadratic equation in the form [tex] ax^2+bx+c=0[/tex] you can use the quadratic formula:
[tex] x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex]
In your case, the equation [tex] x^2-4x+29=0[/tex] is identified by the coefficient choice [tex] a=1,\ b=-4,\ c=29[/tex], so the solving formula becomes
[tex] x_{1,2} = \dfrac{4\pm\sqrt{16-116}}{2} = \dfrac{4\pm\sqrt{-100}}{2} [/tex]
As you can see, we have a negative number under a square root, an operation impossible to perform using real numbers. So, this equation has no real solutions.
