Algebra formulas: answer is positive, but in calculator it's negative.

Question

$$-X^2 + 11X - 30 = 0 $$

$$\frac{-11 + \sqrt{11^2 -4 * 1*30}}{2*1} => \frac{-11 + \sqrt{1}}{2} => -5$$

Why do I get minus? In the book, it shows 5, not -5?

Answer 1

$$-X^2 + 11X - 30 = 0 \iff X^2 - 11x + 30 = (X - 6)(X-5) = 0$$

Either $a = -1,\, b = 11, \;\text{and}\; c = -30\;$

or else $\;a = 1,\, b = -11, \;\text{and}\; c = 30$

Be careful with signs!

$$x_i = \frac{11 \pm \overbrace{\sqrt{(-11)^2 - 4 \cdot 1\cdot 30}}^{\sqrt{121 - 120} = 1}}{2\cdot 1} \iff \frac{11 \pm 1}{2} \iff x = 6, \;\text{or}\; x = 5$$