-17=(1/3)(y+9)

Solution for -17=(1/3)(y+9) equation:

-17=(1/3)(y+9)

We move all terms to the left:

-17-((1/3)(y+9))=0


Domain of the equation: 3)(y+9))!=0

y∈R


We add all the numbers together, and all the variables

-((+1/3)(y+9))-17=0

We multiply parentheses ..

-((+y^2+1/3*9))-17=0

We multiply all the terms by the denominator


-((+y^2+1-17*3*9))=0


We calculate terms in parentheses: -((+y^2+1-17*3*9)), so:

(+y^2+1-17*3*9)

We get rid of parentheses

y^2+1-17*3*9

We add all the numbers together, and all the variables

y^2-458

Back to the equation:

-(y^2-458)


We get rid of parentheses

-y^2+458=0

We add all the numbers together, and all the variables

-1y^2+458=0

a = -1; b = 0; c = +458;
Δ = b2-4ac
Δ = 02-4·(-1)·458
Δ = 1832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1832}=\sqrt{4*458}=\sqrt{4}*\sqrt{458}=2\sqrt{458}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{458}}{2*-1}=\frac{0-2\sqrt{458}}{-2}
=-\frac{2\sqrt{458}}{-2}
=-\frac{\sqrt{458}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{458}}{2*-1}=\frac{0+2\sqrt{458}}{-2}
=\frac{2\sqrt{458}}{-2}
=\frac{\sqrt{458}}{-1}
$