[tex]\huge\underline\mathcal{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
the question asks us to find the values of y.
the question can be solved as follows ~
[tex]\longrightarrow \: 5y {}^{2} - 17y = - 6[/tex]
let's first convert the equation into its general formula , i.e. , ax² + bx + c = 0
[tex]\longrightarrow \: 5y {}^{2} - 17y + 6 = 0[/tex]
using splitting the middle term , let's find out the factors of the given equation ~
[tex]\longrightarrow \: 5y {}^{2} - 15y - 2y + 6 = 0 \\ \\ \longrightarrow \: 5y \: (y - 3) - 2 \: (y - 3) = 0 \\ \\ \longrightarrow \: 5y - 2 = 0 \: \: \: or \: \: \: y - 3 = 0 \\ \\ \longrightarrow \:\boxed{ y = \frac{2}{5}} \: \: \: or \: \: \: \boxed{y = 3}[/tex]
hope helpful ~
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \purple\diamond{\boxed{\boxed{\boxed{\sf{{ \pink{ANSWER}}}}}}}[/tex]
[tex]5y^2- 17y=-6[/tex]
Move terms to the left side
[tex]5y^2- 17y=-6 [/tex]
[tex]5y^2- 17y-(-6) = 0[/tex]
Use the sum-product pattern
[tex]5y^2-17y+6=0[/tex]
[tex]5y^2-2y-15y+6=0[/tex]
Common factor from the two pairs
[tex](5y^2-2y)+(-15y+6) = 0[/tex]
[tex]y(5y-2)-3(5y-2) = 0[/tex]
Rewrite in factored form
[tex]y(5y-2)-3(5y-2) = 0[/tex]
[tex](y-3)(5y-2) = 0[/tex]
Create separate equations
[tex](y-3)(5y-2) = 0[/tex]
[tex]y-3=0[/tex]
[tex]5y-2=0[/tex]
Solve :
Rearrange and isolate the variable to find each solution
[tex]y = 3[/tex]
[tex]y = \frac{2}{5}[/tex]
