y/3+11=y2-3

Solution for y/3+11=y2-3 equation:

y/3+11=y2-3

We move all terms to the left:

y/3+11-(y2-3)=0

We add all the numbers together, and all the variables

-(+y^2-3)+y/3+11=0

We get rid of parentheses

-y^2+y/3+3+11=0

We multiply all the terms by the denominator


-y^2*3+y+3*3+11*3=0

We add all the numbers together, and all the variables

-y^2*3+y+42=0

Wy multiply elements

-3y^2+y+42=0

a = -3; b = 1; c = +42;
Δ = b2-4ac
Δ = 12-4·(-3)·42
Δ = 505
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{505}}{2*-3}=\frac{-1-\sqrt{505}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{505}}{2*-3}=\frac{-1+\sqrt{505}}{-6}
$