# How do you solve x(x-9)+20=0?

May 13, 2016

Develop the equation

${x}^{2} - 9 x + 20 = 0$

Your equation is of the form

$a {x}^{2} - b x + c = 0$

Find the discriminant ($\Delta$)

$\Delta = {b}^{2} - 4 a c$

$\Delta = {\left(- 9\right)}^{2} - 4 \cdot 20 = 1$

$\Delta$ is greater than zero, this means two real roots exist.

$x ' = \frac{- b + \sqrt{\Delta}}{2 a} = \frac{- \left(- 9\right) + \sqrt{1}}{2} = 5$
$x ' ' = \frac{- b - \sqrt{\Delta}}{2 a} = \frac{- \left(- 9\right) - \sqrt{1}}{2} = 4$