Answer :
we have the expression
[tex]10(3t-4)^2+9(3t-4)-9=0[/tex]Let
x=3t-4
Change the variable
so
10x^2+9x-9=0
solve the quadratic equation using the formula
we have
a=10
b=9
c=-9
substitute
[tex]x=\frac{-9\pm\sqrt[]{9^2-4(10)(-9)}}{2(10)}[/tex][tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{441}}{20} \\ \\ x=\frac{-9\pm21}{20} \\ x=\frac{12}{20}=\frac{3}{5} \\ \\ x=-\frac{3}{2} \end{gathered}[/tex]we have
x=3/5 and x=-3/2
Find the value of t
Remember that
x=3t-4
For x=3/5
3/5=3t-4
3t=3/5+4
3t=23/5
t=23/15
For t=-3/2
-3/2=3t-4
3t=-3/2+4
3t=5/2
t=5/6
therefore
the answer is