Answer:
[tex]t=\frac{5-\sqrt{17}}{2},\:t=\frac{5+\sqrt{17}}{2}[/tex]
[tex]t=0.43845\dots ,\:t=4.56155\dots[/tex]
Step-by-step explanation:
[tex]12=2+25t-5t^2[/tex]
[tex]2+25t-5t^2=12[/tex]
[tex]-5t^2+25t-10=0[/tex]
[tex]\frac{-25+\sqrt{25^2-4\left(-5\right)\left(-10\right)}}{2\left(-5\right)}[/tex]
[tex]\frac{-25-\sqrt{25^2-4\left(-5\right)\left(-10\right)}}{2\left(-5\right)}[/tex]
[tex]t=\frac{5-\sqrt{17}}{2},\:t=\frac{5+\sqrt{17}}{2}[/tex]
[tex]t=0.43845\dots ,\:t=4.56155\dots[/tex]
