[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]
[ Multiply both sides by 2 ]
[tex]\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]
[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 289 - ( - 80)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 369[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]
[tex]\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]
