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

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Answer 1 · 2015-05-10T18:09:59

discriminant $D= b^2 - 4ac$

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

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

$D= b^2 - 4ac = (-5^2) - (4 xx 1 xx -6)$
$D= 25 + 24 = 49$

formula for roots :

$x = (-b +- sqrt D) / (2a) = (5 +- sqrt 49) / 2$

$x = (5 +7) / 2 = 12 /2$ and

$(5 -7) /2 = -2/2$

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

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