Question

Solve for Y

5y² - 17y=-6
If there is more than one solution, separate them with commas.
or is there no solution?

Answer 1

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`5y^2- 17y=-6`

Move terms to the left side

`5y^2- 17y=-6`

`5y^2- 17y-(-6) = 0`

Use the sum-product pattern

`5y^2-17y+6=0`

`5y^2-2y-15y+6=0`

Common factor from the two pairs

`(5y^2-2y)+(-15y+6) = 0`

`y(5y-2)-3(5y-2) = 0`

Rewrite in factored form

`y(5y-2)-3(5y-2) = 0`

`(y-3)(5y-2) = 0`

Create separate equations

`(y-3)(5y-2) = 0`

`y-3=0`

`5y-2=0`

Solve :

Rearrange and isolate the variable to find each solution

`y = 3`

`y = (2)/(5)`

Answer 2

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the question asks us to find the values of y.

the question can be solved as follows ~

`\longrightarrow \: 5y {}^(2) - 17y = - 6`

let's first convert the equation into its general formula , i.e. , ax² + bx + c = 0

`\longrightarrow \: 5y {}^(2) - 17y + 6 = 0`

using splitting the middle term , let's find out the factors of the given equation ~

`\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 = (2)/(5)} \: \: \: or \: \: \: \boxed{y = 3}`

hope helpful ~