Question

I need some help please do this

Answer 1

we have the expression

`10(3t-4)^2+9(3t-4)-9=0`

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

`x=\frac{-9\pm\sqrt[]{9^2-4(10)(-9)}}{2(10)}`
`\begin{gathered} x=\frac{-9\pm\sqrt[]{441}}{20} \\ \\ x=(-9\pm21)/(20) \\ x=(12)/(20)=(3)/(5) \\ \\ x=-(3)/(2) \end{gathered}`

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

t=23/15 and t=5/6