# How do you solve t^2 + 5t - 24 = 0 ?

Mar 26, 2016

$x = 3 , - 8$

#### Explanation:

color(blue)(t^2+5t-24=0

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Where

color(red)(a=1,b=5,c=-24

$\rightarrow x = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \left(1\right) \left(- 24\right)}}{2 \left(1\right)}$

$\rightarrow x = \frac{- 5 \pm \sqrt{25 - \left(- 96\right)}}{2}$

$\rightarrow x = \frac{- 5 \pm \sqrt{25 + 96}}{2}$

$\rightarrow x = \frac{- 5 \pm \sqrt{121}}{2}$

$\rightarrow x = \frac{- 5 \pm 11}{2}$

Now we have $2$ solutions

color(purple)(x=(-5+11)/(2)=6/2=3

color(indigo)(x=(-5-11)/(2)=-16/2=-8

:. color(blue)( ul bar |x=3,-8|