7=y+3(y2)

Solution for 7=y+3(y2) equation:

7=y+3(y2)

We move all terms to the left:

7-(y+3(y2))=0

We add all the numbers together, and all the variables

-(+y+3y^2)+7=0

We get rid of parentheses

-3y^2-y+7=0

We add all the numbers together, and all the variables

-3y^2-1y+7=0

a = -3; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-3)·7
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{85}}{2*-3}=\frac{1-\sqrt{85}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*-3}=\frac{1+\sqrt{85}}{-6}
$