# How do you find the discriminant and how many and what type of solutions does x^2 - 5x = 6 have?

May 10, 2015

discriminant $D = {b}^{2} - 4 a c$

the equation can be written as:
${x}^{2} - 5 x - 6 = 0$

here:
$a = 1$
$b = - 5$
$c = - 6$
(the coefficients of ${x}^{2}$ , $x$ and the constant term respectively)

$D = {b}^{2} - 4 a c = \left(- {5}^{2}\right) - \left(4 \times 1 \times - 6\right)$
$D = 25 + 24 = 49$

formula for roots :

$x = \frac{- b \pm \sqrt{D}}{2 a} = \frac{5 \pm \sqrt{49}}{2}$

$x = \frac{5 + 7}{2} = \frac{12}{2}$ and

$\frac{5 - 7}{2} = - \frac{2}{2}$

$x$ has two solutions:
$x = 6$ and $x = - 1$
since $D > 0$ the solutions are real and unequal